The attacking midfielder was entering the final year of his contract at Stade Velodrome and Marseille chose to cash in on the 29-year-old, who has spent the last eight seasons with the Provence outfit.
Although there was interest from the Premier League - with QPR reportedly particularly keen on the winger - as well as a rumoured pursuit from Fiorentina, he has chosen to sign a three-year deal with the Russian outfit.
No details of the fee have been revealed, though it is believed to be in the region of £5.6 million (€7m).
In a statement on their official website, Marseille praised the 37-time capped Les Bleus star, saying: "He fought with all his abilities, his assets: they became his strength, his trademark.
"For all those moments shared, Mathieu deserves thanks. Good luck..."
Amongst his most memorable moments for Marseille was a stunning goal in the Champions League against Liverpool at Anfield in October 2007, which helped the French club to a famous win. In total, he would make 325 appearances for Marcelo Bielsa's club, scoring on 37 occasions.
Dinamo Moscow, who will take part in the Europa League this season, will become his third senior club, having moved to OM from Libourne in 2006 aged 21.
The Russian outfit have already signed Alexander Buttner from Manchester United and William Vainqueur from Standard this summer.