The Netherlands international has agreed to a contract of undisclosed length with the Ligue 1 club, who are coached by former Roma boss Rudi Garcia.
Marseille announced the news with a Twitter video appearing to show the player parachute into the training ground, where he was met by sporting director Andoni Zubizarreta.
The footage ends by showing Strootman in a Marseille shirt, as though he had been playing himself in the popular video game Fortnite.
The midfielder joined Roma – who confirmed the fee, which could rise by another €3m – on a five-year deal in 2013, but he suffered a serious knee injury in 2014 that saw him miss most of the next two years.
He returned to regular football in 2016-2017 and played a key role in his side's run to the Champions League semi-finals last term.
According to some reports in Italy, Strootman had wanted to stay at Stadio Olimpico and broke down when he told his team-mates he had been told he was no longer part of the club's plans.
Roma signed Steven Nzonzi, Javier Pastore and Bryan Cristante to bolster their midfield during the Serie A transfer window.