Antonio Conte has given Moses a chance at Stamford Bridge this season, after the Super Eagles star spent the last three years on loan with Liverpool, Stoke City and West Ham.
The Premier League leaders rewarded Moses with a two-year contract extension earlier this month
Carragher says he did not expect him to turn his Chelsea career around remarkably.
“Another thing you want a manager to do is improve players — and look at Victor Moses. I never expected him to have a future at Chelsea,” Carragher wrote in Daily Mail.
“Given he had been out on loan so much, and the levels he has shown have taken me by complete surprise. He has been excellent in his new role of right wing back.”