Although the deal was not completed before Friday's 11 pm deadline, a deal sheet was submitted for a two-hour extension which allowed Arsenal to sign Sterling, who made 81 appearances for Chelsea but has not played in the new campaign.
Chelsea signed Sterling from Manchester City in a deal worth up to 50 million pounds in 2022 but the player was told in no uncertain terms by Maresca that he would not get any playing time and was welcome to seek a move to another club.
Arsenal boss Mikel Arteta had said earlier this month that he admired Sterling, having worked with the winger during his time as assistant coach at Manchester City.
Sterling's capture will give Arsenal depth on the left wing where he will compete with Gabriel Martinelli and Leandro Trossard for a spot in the starting lineup.
Having started his senior career at Liverpool where he was named the Young Player of the Season twice, Sterling played the majority of his career at Manchester City where he won 10 trophies - including four Premier League titles.
Sterling also has 82 caps for England but he has not played for his country since the 2022 World Cup.
He is Arsenal's fourth summer recruit after goalkeeper David Raya, who made his loan move permanent, defender Riccardo Calafiori and midfielder Mikel Merino.