Lille pipped Paris Saint Germain to the crown by a point on the final day of the season, winning the league for the first time in a decade.
Galtier still had one year remaining on his contract but is keen to experience a new challenge after almost four years in charge.
The 54-year-old took over the club in December 2017 while they were battling relegation and kept them up before finishing second the following campaign.
After finishing fourth in the curtailed 2019/2020 season, Lille broke PSG’s monopoly of Ligue 1 this term, with Sunday’s 2-1 victory at Angers securing the title.
"I made my decision. I informed my president, Olivier Letang, after having listened to him a lot this morning, that I was going to leave LOSC. Or that I was stopping with LOSC, I do not know quite what term to use,” Galtier told L’Equipe.
"I just feel strongly that I have done my time here. That four-year cycle is long enough for a coach. So yes, it's only been five months that I collaborate every day with Olivier Letang and five months is not a lot for a collaboration.
"Having spent four years here, I feel inside that it's time to leave this beautiful club, this magnificent club."
He added: "My decision is not linked to the final ranking of the team, if we had finished fourth or seventh I would have made the same decision.
"I do not want to leave on a success. I am leaving because I have decided that after four years it is time to leave. I spent eight and a half years at Saint-Etienne, including seven and a half at the head of the team, it was good.
"I'm leaving Lille with an incredible result, I need something else. I don't want to fall into a routine, into something classic, as I experienced at one point in Saint-Etienne. Wear and tear, always being in the same environment."
Galtier has been linked with the likes of Nice, Olympique Lyon and Napoli following his exit from the Stade Pierre-Mauroy.
