The 19-year-old left Elland Road in January, despite having impressed for the Whites at various youth levels following his move from Everton.
He linked up with his former Leeds coach Mark Jackson at Milton Keynes Dons, although could not prevent the club suffering relegation to League Two last season.
Jackson was axed but Dean remained and has made 11 appearances in all competitions this season.
His most recent goal, scored in a 3-2 win over Swindon Town, has taken his tally for October to four.
It follows a brace against Barrow and a strike in a win over Bradford City.
Speaking after Dean joined the Dons, Jackson said: “I’ve known Max for a long time and was involved in bringing him to Leeds United from Everton.
"During my time working with him, he showed his capabilities, performing way above his age group with the under-23s.
“When this opportunity came up this month, it was important we acted on it quickly as I know there were a number of other clubs looking to sign him.
"Ultimately, he wanted to come here and he is really excited by this opportunity.
“He has got huge potential and he’s certainly one for the future but I’m also confident that, given his qualities, he is someone who can have an impact for us in the immediate term as well.”