Gomis has been brought to Hearts by director of football Levein and head coach Robbie Neilson as they challenge Rangers and Hibernian for the Scottish Championship title.
Levein took Gomis to Tannadice from Cowdenbeath and the midfielder went on to win the Scottish Cup before earning a move to Birmingham. He had a second spell with United last season.
Gomis told Hearts TV: "He (Levein) is the reason why I'm here. He signed me for Dundee United and the player I am today is because of him.
"I thank him very much for that and hopefully I can repay the favour by playing well week in, week out."
The 28-year-old becomes Hearts' most experienced player and Levein and Neilson have asked him to help school the young players at the club.
Gomis, who has been capped by Senegal, said: "I spoke to the manager and he told me what he wants me to do in the club, like looking after the players, so it's a big responsibility but I'm looking forward to it. Hopefully I can show a good example to them.
"It's a great challenge. The manager has put a lot of faith in me and I'm going to do my best and hope the young boys learn from me."