The 21-year-old, who has joined for an undisclosed fee, is the eighth new arrival at Turf Moor in the summer transfer window.
"I'm very excited. Very happy to be here and I can't wait to see the fans," he said.
"After speaking to the coach (Scott Parker), the project sounded good to me and hopefully we can make it a success."
Mejbri joined arrived at Old Trafford in 2021 - the same year he made his Tunisia debut - and spent loan spells at Birmingham and Sevilla.