Defender Rugani arrives from Juventus, where he made 101 appearances across all competitions and won the Italian title five times, as well as the Coppa Italia on three occasions.
The centre-back has struggled to become a first-team regular at Juve, though, making just 22 league starts across the previous two campaigns.
Rugani will now spend the 2020-2021 season on loan at Rennes, as is also the case with full-back Dalbert, who has completed his move from Inter Milan.
Les présentations sont faites ! 😉 pic.twitter.com/Ef8hHLNSiL— Stade Rennais F.C. (@staderennais) October 3, 2020
The Brazilian, who revealed he decided to join after speaking to former Vitoria Guimaraes team-mate and current Rennes winger Raphinha, returns to Ligue 1 having previously played in France with Nice.
"I'm happy to have had this opportunity to join Rennes," Dalbert said. "I hope to have a good season with my new team-mates.
"Raphinha being here, I followed the matches of the club, it works well. I spoke with him before coming - he told me a lot of good things about the city and the club. I am very happy to be here."
Rennes has made an excellent start to the new term, picking up 13 points from five Ligue 1 games to sit top of the table.
This season will also seem it embark on its first ever campaign in the UEFA Champions League, having been drawn alongside Chelsea, Sevilla and Krasnodar in Group E.