The 19-year old midfielder finds himself with the League One side on a youth loan which will run for the rest of the season.
Baker just returned to Stamford Bridge following a temporary spell with Sheffield Wednesday and his arrival at mk:stadium has manager Karl Robinson in high spirits following the injury to young gun Dele Alli.
"Lewis is one of the most gifted young midfielders in England and I'm looking forward to working with him for the rest of the season," Robinson told the club's official website.
"Obviously with Dele out for up to six weeks, Lewis gives us another option in midfield. He also knows where the goal is too, which is clear by the amount he scored last season (26 in Chelsea's youth teams) - a great achievement at any age level.
"I am confident that this addition will give us a real push at an important time in the season."
Chelsea FC (@ChelseaFC) February 25, 2015
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