Sir Robin came third in the Rhum class as he crossed the finish line at Pointe a Pitre at 4.52pm local time/8.52pm GMT after 20 days, 7 hours, 52 minutes and 22 seconds at sea. He managed to hold off rival Wilfrid Clerton, who was 20 miles behind.
When he last sailed in the race 32 years ago he finished in 14th place in a time of 20 days, 20 hours, 20 minutes.
The first man to sail solo, non-stop round the world in 1968/9 said he was happy to finish the 3,542 mile race after the "intense" contest for the final podium place.
He sailed the 3,542 mile (Rhumb line) course at an average speed of 7.26 knots but in reality he actually did 4,416 miles at an average of 9.05 knots.
Sir Robin, who founded the Clipper Round the World Yacht Race, returned to his solo ocean-racing roots by entering his Open 60 yacht Grey Power into the Route du Rhum competition which started today in St Malo, France.
The veteran sportsman, who was the oldest participant, last competed in the 3,542-mile race from St Malo, France, to Guadeloupe in the Caribbean in 1982 in his 70ft catamaran Olympus.
And this is his first solo race since his Velux 5 Oceans circumnavigation in 2006-7, which he also sailed in Grey Power.
The first man to sail solo, nonstop round the world in 1968/9 is currently in fourth place on his Open 60 Grey Power. He is just three miles from the third-placed yacht, having dropped down a place this morning after holding onto third for almost 36 hours.
Sir Robin is involved in a “stimulating” battle with three other yachts for the final podium in a week which has seen light winds, rain squalls and big wind shifts in the Azores high pressure system.
Sir Robin, who founded the Clipper Race at his base in Gosport, Hampshire, has 1,253 miles to go till the finish line. He set off from Saint-Malo, France, on 2 November on the 3,542 mile Transatlantic contest.
The fight for third is very exciting. It has been a frustrating week at times though. The North Atlantic depressions pushed the Azores high South after the big yachts had passed through.
This meant I had to go deeper South to avoid it, which means a greater distance to the finish. We have all been battling lighter than forecast winds, rain squalls and big shifts in the wind, but we are in the Tropics after all.
Sir Robin Knox-Johnston has set off on a solo transatlantic race today.
The veteran sailor is competing in the Route du Rhum race from St Malo in France - forty-five years after he became the first man to sail alone non-stop around the world.
Sir Robin, who is based in Hampshire, founded the Clipper Round the World Yacht Race.
"There are bound to be questions about my age. They ask what I think of doing this at 75 and I say I am still 45. That is how I feel. I think I am 45 and that is where I stay. I feel no different to when I last raced. I am pretty fit. I lead an active life. I think of myself as young and that is it. I treat myself as young and I am just not ready for the slippers, pipe and television. That is not coming in a hurry."
It is known as the toughest sailing race in the world. The Volvo Ocean Race begins tomorrow - and for the first time in 12 years an all-female crew will compete for the title. The sailors - many of whom are from the south coast - are currently preparing for the race start at the Spanish port of Alicante, from where Sally Simmonds reports.
The Volvo Ocean Race leaves Alicante this weekend. We will have a full package later - this is a preview.
Many who take to the water rely on the RNLI lifeboats to come to their aid if they get into trouble - including professional sailors. Now one of them, Hannah White, is hoping to help the RNLI by rowing from the West of the country to the East - ending in Gravesend. And she's doing it in a kayak. Hannah joined Fred from our London studio.
Video of the Sevenstar Round Britain and Ireland fleet setting off from Cowes this morning and racing up the Channel. Interviews with Dee Caffari from Team SCA and Ian Walker from Team Abu Dhabi - both Hampshire sailors taking part in this event and the Volvo Ocean Race in October