On October 28, the National Hurricane Center (NHC) started watching the Southwestern Caribbean. There was an area that might become a tropical cyclone. At 12:00 UTC on October 29, the area of interest turned to two tropical waves coming together moving into the Eastern Caribbean, still supposed to enter the region. The disturbance steadily moved westward into a better environment for development. This allowed it to become better organized on October 31, but there was some question as to if it had formed a good circulation. However, by 21:00 UTC that day, satellite and microwave imagery said that a circulation had formed, and the NHC began issuing advisories on "Tropical Depression Twenty-Nine". At 03:00 UTC on November 1, the system intensified into "Tropical Storm Eta", becoming the earliest 28th non-extratropical storm on record in an Atlantic hurricane season, beating Tropical Storm Zeta in 2005.
Continuing west because of a ridge, Eta slowly organized throughout the day as cold convection began to form on top of its center. After barely holding onto tropical storm strength for 15 hours, Eta began to intensify quickly, reaching hurricane status at 09:00 UTC on November 2. Six hours later, the storm turned into a high-end Category 2 hurricane as a tiny eye became apparent in satellite imagery. Eta then reached Category 3 status at 18:00 UTC before becoming a Category 4 hurricane three hours later, with lots of lightning being observed in its eyewall. Eta begun to slow down and turn west-southwestward because of a ridge over the United States. At 03:00 UTC on November 3, a airplane found the system still intensifying quickly with winds of 150 mph (240 km/h) and a pressure of 927 mbar as it still slowed. According to the NHC, Eta maintained its peak winds as it reached its lowest pressure of 923 mbar at 06:00 UTC, marking its peak intensity as a strong Category 4 hurricane. "The Washington Post" said that several experts thought Eta peaked as a Category 5 hurricane based on satellite imagery as well as a lack of aircraft due to several issues. Still in a in a good location, Eta began to weaken six hours after its peak because of an eyewall replacement cycle, which it completed as it made landfall at 21:00 UTC south of Puerto Cabezas, Nicaragua, with winds of 140 mph (225 km/h) and a pressure of 940 mbar. Land caused Eta to rapidly weaken as it moved slowly west after landfall with its eye disappearing and its convection weakening. It fell below major hurricane status just three hours after landfall at 00:00 UTC on November 4. Eta continued to weaken rapidly, dropping to tropical storm status at 09:00 UTC, and to a tropical depression at 00:00 UTC on November 5.
Even though the storm was messy, Eta still held on to tropical cyclone status, and began turning northeastward, eventually moving back over the Caribbean Sea on November 6 and speeding up due to the influence of a developing trough over the Gulf of Mexico. On November 7, following a couple of center reformations, the system became better organized and became a tropical storm again, at 15:00 UTC on November 7. Even with strong wind shear, the storm continued to strengthen through the day and reached a second peak of winds of 65 mph (100 km/h) and a pressure of 991 mbar at 00:00 UTC on November 8. It then held its strength and slowed slightly before making landfall on the south central coast of Cuba at 09:00 UTC. Eta weakened after making landfall in Cuba's Sancti Spíritus Province, but this was short as it quickly moved back over water in the Atlantic Ocean and began to strengthen again as it turned northwestward around the northeastern side of a low that had formed over the northwestern Caribbean Sea near the Isle of Youth.
Eta briefly gained a eye feature before bad conditions removed most of its convection, although the storm was able to maintain its intensity as it grew in size and approached South Florida. At 04:00 UTC on November 9, Eta made its third landfall on the Lower Matecumbe Key in the Florida Keys with the same intensity as its Cuban landfall. It then passed just south of the southwestern coast of Florida as it turned westward. Eta then turned southwestward under the influence of a strong ridge across the Gulf of Mexico, Florida, and near the US East Coast. This also brought it into an area of really dry air, causing the storm to weaken and its area of gale-force winds to shrink. However, even after its center became sheared to the west of its convection, Eta began to intensify again over the warm waters of the Gulf. Eta than began to speed up north-northeast around the western edge of a subtropical ridge as its center reformed under the convection and an eye formed. Eta then regained minimal hurricane status at 12:35 UTC on November 11, reaching a fourth peak intensity with winds of 75 mph (120 km/h) and a pressure of 983 mbar.
Shortly after its peak, dry air rapidly removed the convection and caused the eye to be gone, causing Eta to weaken back into a tropical storm at 18:00 UTC. The system turned further east and made landfall near Cedar Key, Florida at 09:00 UTC on November 12, with winds of 50 mph (85 km/h). The storm weakened over land as it sped toward the north-northeastward, eventually emerging over the waters of the Atlantic near the Florida–Georgia border at 18:00 UTC. Eta came out with winds of 40 mph (65 km/h) before restrengthening as it began its extratropical transition. The storm completed its transition on November 13. On the next day, Eta was absorbed into another frontal system to the north.
Early on November 1, important people in Honduras and Nicaragua put in Hurricane Watches and Warnings for the northeastern coast of Honduras from Punta Patuca to Nicaragua and the northeastern coast of Nicaragua from the Honduras border to Puerto Cabezas. Later that day, a hurricane warning was put in from the Honduras–Nicaragua border (place where Honduras and Nicaragua meet) to Sandy Bay Sirpi, while a tropical storm warning was put in for areas from Punta Patuca to the Honduras–Nicaragua border. A tropical storm watch was also issued from west of Punta Patuca westward to Punta Castilla late that same day.
Some people were worried that of storm surge along the coastline may happen, so Nicaraguan President Daniel Ortega issued a yellow alert for most of the western departments on October 31, which were upgraded to a red alert by November 2. People in coastal towns were told to leave as supplies, including 88 tons of food, sleeping bags, hygiene kits, and plastic, were brought to Puerto Cabezas according to SINAPRED. The navy of Nicaragua helped more than 3,000 families from offshore islands to Puerto Cabezas as people in the city waited in long lines to access cash machines while getting supplies. Just before the storm's arrival, the army of Nicaragua moved red-helmeted troops to Puerto Cabezas to help in search and rescue efforts that would happen because of Eta. More than 10,000 people were at shelters in Puerto Cabezas and surrounding villages to wait out the storm.
Alerts were placed for all of Honduras The Honduran Air Force told two planes to send 4,000 pounds of food to La Mosquitia, Gracias a Dios. The National Police of Honduras was told to tell passengers of roadways blocked by a landslide or flooding. More than 20,000 pounds of food were stored at the Offices of Risk Management and National Contingencies in San Pedro Sula, ahead of the storm. Because of Hurricane Eta, in order to limit movements and protect human lives, the Honduran government canceled the Morazanico national holiday.