Swimming is an excellent exercise for your back problem. Since you had the problem 7 years ago, your root problem now must be stiff joints, ligaments and weak muscles. The buoyancy of the water will make you feel lighter and make your movements easier. The resistance provided by water helps to strengthen the muscles and also aids in stress reduction, minimum muscular strain and cardio-vascular improvement.
When you are chest deep in water, the load on the joints is 25% your body weight and if you are neck deep in water, the load on joints is just 10% of your body weight. So, the joints do not feel the impact of the body weight in water. Water provides a balance to the body. Lax muscles are strengthened and those that are tight are stretched by buoyancy of water.
You can start with 10-15 minutes of swimming and gradually go up to 25-30 minutes. Amount of calories burnt could be 150-200 calories in 25-30 minutes which is much higher than exercising on land.