United States international Olosunde, 21, was released by the Old Trafford outfit at the end of last season and was also linked with a number of clubs in Major League soccer.
Philadelphia-born Olosunde, who has been capped once by the US, was a key player for the Red Devils' under-23s before suffering a long-term injury in February 2018 which sidelined him until January.
Predominantly a right-back, Olosunde - who has previously played for New York Red Bulls reserves - also offers versatility across the back line and is capable of playing as a central defender, left back or right-sided midfielder.
Olosunde, who is contracted with the Millers until the summer of 2021, is the club's sixth signing of the summer and second of the week following the addition of Newcastle United midfielder Dan Barlaser on a season-long loan.
Striker Freddie Ladapo, midfielder Shaun MacDonald, French winger Julien Lamy and forward Carlton Morris are the club's other signings so far in the close season.