The Blues announced their second summer signing this morning, with the 38-year-old following Jorginho to Stamford Bridge.
Green, who penned a one-year contract at Chelsea, will provide back up for Thibaut Courtois and Willy Caballero.
However, Chelsea fans are bemused by Maurizio Sarri’s latest signing, which could result in Courtois heading to Real Madrid this summer.
One fan wrote on Twitter: “He can’t even hold the jersey right.”
A fellow Chelsea supporter added: “Love how they had to reassure the fans that he’s joining as a backup.”
Meanwhile, one fan joked that Green is a much better signing than Liverpool’s world-record buy Alisson.
He tweeted: “Green > Alisson.”
Other fans called for Chelsea to splash the cash following Green’s arrival, urging Sarri to raid Serie A.
“Announce Higuain, Rugani, and Pjanic,” a supporter replied to Chelsea’s announcement.
On his move to Chelsea, Green said: “It has been a whirlwind 24 hours.
“You are thinking about your career and where you want to go and then you get a phone call like this, and it is a short conversation.
“It has been a pretty dramatic time for me and I can’t wait to get started.
“I am absolutely delighted and it is a thrill and an honour to be here.”