"Jason is a determined leader, a tough-minded competitor and a great team mate," Bucks owners Wesley Edens and Marc Lasry said in a statement. "We believe his focus, vision and intensity will help him...to rebuild the Milwaukee Bucks as we aspire to achieve excellence over the next several years. We are excited Jason will call Milwaukee his new home."
Kidd was appointed after the Brooklyn Nets freed him from his contract in exchange for a pair of second-round draft picks in 2015 and 2019.
He takes over from Larry Drew who was fired on Monday after leading the team to a 15-67 record in the first year of his three-year deal.
Kidd, 41, enjoyed a stellar 19-year playing career as a point guard before taking on his first head coaching job at the Nets.
He guided the team to a 44-38 record last season and won a first-round playoff series against Toronto in the first campaign of a $10.5 million, four-year deal.
His appointment by the Bucks was initially signaled when Kidd proclaimed after last week's NBA Draft, held at the Nets' Barclays Center, that he wanted more authority in Brooklyn.
The terms of his contract with the Bucks were not disclosed.
Lasry is a former Nets minority owner who bought the Bucks with Edens for $550 million this year and once served as a financial adviser to Kidd.
Besides putting a new coach in place, the Bucks have also kept young All-Star point guard Kyrie Irving by agreeing terms with him on a contract to be signed on July 10, ESPN reported.
Irving, 22, tweeted that he was "super excited" to be part of the organization for the long term.
Lionel Hollins, George Karl, Mark Jackson and Ettore Messina are being touted as possible replacements for Kidd at the Nets.
(Writing by Larry Fine, editing by Tony Jimenez)