"The 22-year-old English Under-21 international defender has joined the club after successfully completing his medical," said the Ligue 1 club on their website.
Egan-Riley came through the youth system at Manchester City before joining Burnley. After loan spells at Hibernian in Scotland and PSV Eindhoven, he became a first-team regular as Burnley won promotion to the Premier League last season. He was selected to the Championship team of the season.
Marseille described Egan-Riley as "solid and composed in build-up play", and as "versatile and capable of playing both centrally and on the right side of defence".
Egan-Riley is with the England under-21 squad at the European championship in Slovakia and was an unused substitute as they opened their title defence with a 3-1 win over the Czechs.
Egan-Riley is Marseille's second summer signing, following another out-of-contract Englishman, midfielder Angel Gomes from Lille.
The summer transfer window officially opens in France on Monday, after an initial 10-day window on June 1-10, linked to the Club World Cup.