Roma confirmed the signing of Swedish goalkeeper Robin Olsen from Copenhagen as a replacement for Alisson, who joined Liverpool last Thursday.
Alisson became the most expensive goalkeeper in history when he moved to Liverpool for €62.5 million, while Olsen has cost Roma for €8.5m with performances related bonuses which could see the deal rise by up to €3.5m.
Roma also confirmed that Copenhagen retain the right to 10 percent of any profit should the Sweden No. 1 be sold in the future.
"I'm feeling happy, I'm very excited," Olsen said. "It's a big honour to come to AS Roma. It's the next step for me and I cannot wait to get started."
Olsen, 28, had spent the majority of his career in Scandinavia -- he played for Greek side PAOK in the 2015-16 season -- and had the option to play for Denmark at international level. However, he chose Sweden and started all five matches as they reached the World Cup quarterfinals in Russia.
Roma sporting director Monchi, who is a former goalkeeper himself, had claimed earlier in the window that Alisson "will only leave Roma if I come out of retirement." However, the Brazilian has now signed for Liverpool and Monchi was pleased with the addition of Olsen.
"Robin is a goalkeeper with international experience, and I think he can bring that level to Roma with him," Monchi said. "I am confident he can build on the quality that has seen him firmly establish himself as Sweden's No. 1."
Roma's next preseason match is against Tottenham in the International Champions Cup on Thursday, before a grudge match with Barcelona, where Malcom -- who moved to the Nou Camp ahead of the Italian capital side -- could make his debut.