The former Italy midfielder - who represented the likes of Barcelona, Paris Saint-Germain, Inter Milan and Atletico Madrid during his playing heyday - has joined the Bianconeri on a three-year deal until the end of the 2026-27 season.
Motta steps into the shoes of the highly-successful Allegri, who won a total of 12 trophies during two separate spells in Turin, including the 2023-24 Coppa Italia title with a 1-0 victory over Atalanta BC in the final.
However, Juventus' title celebrations were overshadowed by an Allegri meltdown, as the 56-year-old - who was sent off during the final - allegedly verbally threatened officials and also snubbed sporting director Cristiano Giuntoli.
Juventus - who had been expected to fire Allegri for some time anyway - confirmed the Italian's sacking just a couple of days later, citing "certain behaviours" during the final that were "deemed incompatible" with the club's values.
Motta vows to "keep the Juventus flag flying high"
Juventus ramped up discussions with Motta once Allegri had been given the boot, and Bologna confirmed before their final game of the Serie A season that the erstwhile midfielder would be leaving the club this summer.
Now, Motta has been officially appointed the new head coach of the Bianconeri after an astounding campaign at Dall'Ara, where he led Bologna into the Champions League with a fifth-placed Serie A finish.
Motta's Bologna outfit finished just two places and three points worse off than Juventus in the standings, and their ranking sufficed for UCL qualification thanks to Italy's UEFA coefficient.
"I am really happy to begin a new chapter at the helm of a great club like Juventus. I thank the owners and the management, who can be sure of my ambition to keep the Juventus flag flying high and to please the fans," Motta told the official Juventus website.
The 41-year-old had previously taken charge of Spezia and Genoa before his successful two-year spell at Bologna, whom he led to 35 victories from his 76 matches at the helm.
Which players could Motta sign for Juventus?
As well as having their head coach poached from their ranks, Bologna are also braced for an influx of bids for some of their prized assets, many of whom should be allowed to go for the right price.
One man heavily tipped to follow Motta to the Allianz Stadium is 22-year-old centre-back Riccardo Calafiori, who is reported to have agreed personal terms with the Bianconeri, but Bologna are demanding €30m (£25.4m) to let him depart.
Dutch attacker Joshua Zirkzee is unlikely to follow Calafiori to Juventus, though, as the Old Lady are not in desperate need of a new number nine, allowing Arsenal, Manchester United and AC Milan to battle for the 23-year-old.
Instead, a fresh face in goal and in midfield are set to arrive, as negotiations to sign Monza number one Michele Di Gregorio and Aston Villa's Douglas Luiz are thought to be progressing well.
Weston McKennie and Samuel Iling-Junior are set to head in the opposite direction in the Luiz deal, although Manchester United outcast Mason Greenwood could arrive as a replacement for the latter amid claims that he has also given the thumbs-up to joining Motta's side.