Answer by taking a quote from the following article:

Reginald Martinez Jackson (born May 18, 1946) is an American former professional baseball right fielder who played 21 seasons for the Kansas City / Oakland Athletics, Baltimore Orioles, New York Yankees, and California Angels of Major League Baseball (MLB). Jackson was inducted into the National Baseball Hall of Fame in 1993. Jackson was nicknamed "Mr. October" for his clutch hitting in the postseason with the Athletics and the Yankees. He helped Oakland win five consecutive American League West divisional pennants, three consecutive American League pennants and three consecutive World Series titles, from 1971 to 1975.

Jackson became a free-agent again once the 1981 season was over. The owner of the California Angels, entertainer Gene Autry, had heard of Jackson's desire to return to California to play, and signed him to a five-year contract. On April 27, 1982, in Jackson's first game back at Yankee Stadium with the Angels, he broke out of a terrible season-starting slump to hit a home run off former teammate Ron Guidry. The at-bat began with Yankee fans, angry at Steinbrenner for letting Jackson get away, starting the "Reg-GIE!" chant, and ended it with the fans chanting "Steinbrenner sucks!" By the time of Jackson's election to the Hall of Fame, Steinbrenner had begun to say that letting him go was the biggest mistake he had made as Yankee owner. That season, the Angels won the American League West, and would do so again in 1986, but lost the American League Championship Series both times. On September 17, 1984, on the 17th anniversary of the day he hit his first home run, he hit his 500th, at Anaheim Stadium off Bud Black of the Royals. In 1987, he signed a one-year contract to return to the A's, wearing the number 44 with which he was now most associated rather than the number 9 he previously wore in Oakland. He announced he would retire after the season, at the age of 41. In his last at-bat, at Comiskey Park in Chicago on October 4, he collected a broken-bat single up the middle, but the A's lost to the White Sox, 5-2. Jackson was the last player in the major leagues to have played for the Kansas City Athletics.

how did he join the angels
Gene Autry, had heard of Jackson's desire to return to California to play, and signed him to a five-year contract.