The Gunners confirmed the arrival of Lucas Torreira on Tuesday from Sampdoria.
Leaked video footage showed Lorient teenager Matteo Guendouzi putting pen to paper and Greenwood has also confirmed his move to the Emirates.
Greenwood, 16, has attracted interest from Manchester United but he will playing his football in north London next season.
"Today is the start of a new chapter in my life signing for Arsenal and I can't wait to get started, I'm looking forward to the challenges ahead," he posted on Instagram.
"Leaving Sunderland after 10 years, the club I love and support was a very hard decision.
"I have met some special people along the way, big thanks to Sunderland and all coaches past and present for everything they have done for me.
"I will never forget my roots."