Viviani, who is moving from French WorldTour team Cofidis, left Ineos at the end of 2017 after it was clear he was not going to get the support needed to become a world-class sprinter.
He joined Belgian team, Deceuninck - Quick-Step where he racked up 29 of his 85 victories before joining Cofidis. He did not win once in 2020 but has gone on to win seven times on the road in 2021.
The Italian said he knew he would return to the British team one day after leaving.
Viviani said: "From the moment I left the team, I had in my head that one day I would come back - and now that day has come and I couldn’t be happier,
"In my years away, I’ve never lost contact with the team – with Dave [Brailsford], Rod [Ellingworth], and with the Italian riders and coaches. I am really good friends with lots of the team members and especially Dave.
"I never missed an opportunity to speak with him at races about cycling, my team, my season, and this team. This feels like coming back to a family for me."
In his time at the then-named Team Sky, Viviani took some major wins including a stage of the Giro d'Italia, the Bretagne Classic, and the Cyclassics Hamburg, and many more besides despite not having an out-and-out lead-out train.
"Next year the goal is to win as many races as I can because that’s the job of a sprinter," continued Viviani.
"But I can also support the young group of Grenadiers and pass on my experience. I hope I can be an example to follow and an experienced guy around the incredibly talented young group that is being built."
His new contract brings him up to the next Olympic Games which will be held in 2024 in Paris which gives him plenty of time and stability alongside fellow Italian Olympic star Filippo Ganna.
Deputy team principal, Rod Ellingworth said: "We are delighted to be able to welcome Elia back to the team. We value him as an experienced rider who can win races, but also as a person.
"He brings so much to any group he is a part of, and we hope he can inspire, drive and educate our developing group of riders. Above all though, Elia is a racer, and we can’t wait to see him winning as a Grenadier."
Viviani won Olympic gold in the Omnium in Rio 2016 but was unable to defend his title at Tokyo 2020, losing out to British rider, Matt Walls, who rides for Bora-Hansgrohe on the road.
The 32-year-old referenced his compatriot Ganna and how he had yet another phenomenal season with Ineos and then went on to dominate the Olympics and perform well at the Track World Championships too.
Viviani also gave a lot of credit to Ineos saying that his gold medal in 2016 partly belonged to the team as they supported him all the way through.
"I’ve had a tough two years and the Olympics gave me back what I’ve missed - the legs, confidence, conviction and belief in myself," he said. "My Bronze medal this year has given me the belief to step up to my level again.
"I think this is the best place for me to be at this stage in my career. I’ve done everything I can to come back and I feel proud as a person that I left on good terms and left something good here. Now that’s paid off."
Viviani is the last of four signings announced in one day by Ineos with Omar Fraile being the next highest profile rider to join the squad in 2022.
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