"Ronaldo? He's back with great motivation," Allegri told a press conference of the five-time Ballon d'Or winner who had been linked with a move to Paris Saint-Germain.
Serie A: Juventus superstar Cristiano Ronaldo undergoes medical ahead of fourth season with Turin club
The 36-year-old Portugal international, who has one-year left on his contract, flew back to northern Italy on Sunday night.
He scored two goals in 21 games in Madrid before joining Milan last season on loan, scoring seven goals in 39 appearances for the northern Italian outfit.
"AC Milan are delighted to announce the permanent signing of Fode Ballo-Toure from AS Monaco," last season's Serie A runners-up said in a statement.
The news follows a two-year transfer ban imposed on the club Friday by FIFA for bringing underage Nigerian players to Italy in breach of national immigration laws
The 34-year-old World Cup winner underwent a medical on Friday before signing with the Serie A runners-up who return to the Champions League next season after a seven-year absence.
The US-owned outfit will not be allowed to sign new players for four transfer windows starting from next January 2022, along with two northern amateur sides.
Serie A: AC Milan director Paolo Maldini confirms Olivier Giroud's arrival, regrets Gianluigi Donnarumma exit
Olivier Giroud, a World Cup winner, is reported to be set to sign a two-year contract worth three million euros per season with the Serie A runners-up, who open next season at Sampdoria.
Ronaldo's future had been in doubt after a difficult campaign during which Juventus lost their Serie A crown after nine years, exited the Champions League in the last 16 and only sealed fourth place and elite European football on the final day.
The Milan derby between Inter and AC Milan will take place on matchday 12 on 7 November with the return leg on 6 February.
The 33-year-old becomes new Portuguese coach Jose Mourinho's first signing in a deal that runs until June 2024 and is worth an initial 11.5 million euros ($13.5 million) plus bonuses, the club said.
"Giroud is expected to be in Italy on Thursday to undergo medicals and sign the contract," wrote Sky Sport on its website.
Serie A: Lazio boss Maurizio Sarri says city rival Jose Mourinho’s glittery managerial past ‘doesn’t count for anything’
Mourinho will coach Roma while Sarri takes charge of city rivals Lazio, both housed in the same stadium in the Italian capital.
"The agreement also includes an obligation for Marseille to make the transfer permanent based on the fulfilment of certain requirements."
Spinazzola picked up the injury during Friday's 2-1 Euro 2020 quarter-final win over Belgium in Munich, the day Mourinho arrived in Rome.
Waving the club's yellow and red scarf, Mourinho briefly addressed the crowd before being driven away to the club's Trigoria training centre for the first time.
Serie A: 'Fans, I'm coming,' Jose Mourinho set to arrive in Italian capital as AS Roma hope to end 20-year drought
Mourinho had only been out of work for 15 days after leaving Tottenham two months ago before his return to Serie A was announced on a three-year deal.
The 23-year-old, currently playing in the Copa America with Argentina for whom he has eight caps and two goals, has signed a five-year deal until June 2026.
The 27-year-old midfielder told Turkey's TRT Spor that he will be in Milan on Tuesday to sign a contract after completing a physical with his new team.
Gattuso was appointed as Fiorentina boss on 25 May less than 48 hours after announcing his departure from Napoli and had not been expected to start work until 1 July.