The Italy international completed his move to the Stadium of Light for a fee in the region of £7m from Juventus this summer.
"It has been two good weeks and I came here with a lot of excitement. I am going to give my best of myself to the gaffer," Giaccherini told the club's official website.
"Because I played in the Confederations Cup I did not have much time to rest with only ten days' holiday. But I still made myself available straight away for the team.
"I first met my team in Peschiera del Garda and we have had a good pre-season. I am still not 100% fit, but we will work toward this."
Sunderland begin their Premier League campaign against Fulham on August 17.