Terms of the deal were not immediately disclosed.
Jenkins has spent the last six seasons coaching under Mike Budenholzer, spending five years with the Atlanta Hawks (2013-18) and one with the Milwaukee Bucks (2018-19).
Milwaukee finished with an NBA-best 60 wins this past season and came within two victories of the NBA Finals.
Memphis fired J.B. Bickerstaff in April while demoting former general manager Chris Wallace to scout following a second consecutive season without a playoff appearance. Bickerstaff went 48-97 after taking over for David Fizdale early in the 2017-18 campaign.
Jenkins will be expected to help right the ship.
Prior to the last two seasons, the Grizzlies had made seven consecutive postseason appearances as Mike Conley and Marc Gasol led the way. Gasol was dealt to the Toronto Raptors prior to the trade deadline this past season, while Conley remains, though Memphis did reportedly shop him at the deadline.
Conley's future in Memphis remains uncertain, especially considering the team owns the second overall pick in the 2019 NBA draft. ESPN's Jonathan Givony reported in mid-May that the Grizzlies have made it known they will draft Murray State point guard Ja Morant.
Regardless of Conley's status, bringing in a top prospect like Morant will give Jenkins a potential franchise cornerstone to work with from the start.