The financial details were not disclosed by either club, but British media reported that the pair were signed for a combined fee of more than 50 million pounds ($64.32 million).
The contract includes the option to extend for a further year for both players, United said.
The pair started their youth careers at Dutch side Ajax Amsterdam and went on to play under now-United manager Erik ten Hag in the first team.
The 25-year-old De Ligt won the Eredivisie in the 2018-19 season with Ajax, the Serie A title in 2019-20 with Juventus and the Bundesliga in 2022-23 with Bayern.
"Erik ten Hag shaped the early stages of my career, so he knows how to get the best out of me and I cannot wait to work with him again," De Ligt said in a statement.
"I know what it takes to succeed at the highest level, and I'm determined to continue that record at this special club."
Mazraoui, 26, joined Bayern from Ajax in 2022 and went on to make 55 appearances across all competitions, winning the Bundesliga and the DFL-Supercup in his debut campaign. He was briefly sidelined by injury last season.
"Erik ten Hag played an important part in my development as a player, so it is exciting to be reuniting with him as I enter the prime years of my career," Mazraoui said.
"I know what he expects from his players, and I will give everything to help the group be successful."
