Reports in the British media on Thursday claimed Gerrard will confirm his intention to leave Liveprool when his contract expires in June, with a switch to MLS side LA Galaxy mooted.
Carragher appeared to confirm the news on Twitter, while also giving the move his stamp of approval.
"Sad day for Lfc & English football with the Gerrard news, I think it's the right decision all things considered," the former defender wrote.
Carragher and Gerrard effectively grew up together having both come up through the junior ranks at Liverpool and playing 15 years together in the senior team before the former retired in 2013.
Gerrard's future at Anfield has become a big discussion topic this season with the 34-year-old captain having been left on the bench for key games.
The midfielder, who has only ever played for the club he supported as a child, started on the bench in November for the 16th anniversary of his senior debut as well as Liverpool's away match against Real Madrid in the UEFA Champions League.
Manager Brendan Rodgers has started Gerrard in 17 of 20 Premier League matches this season, plus five of Liverpool's six matches in the Champions League, but that has not stopped stories about the likelihood of the captain leaving his hometown club from bubbling under the surface.
Gerrard scored a brace - both from the penalty spot - in Liverpool's 2-2 draw with Leicester City on Thursday in his 697th senior appearance for the Anfield outfit.
