Speaking about Vettel's announcement on Thursday, Hamilton said he was 'really happy' for Vettel and said that F1 needed a driver of his calibre to stay in the sport.
Hamilton noted how much of a difficult decision it could have been for the four-time world champion to consider a switch to the team, but praised the team also for being able to sign the German.
"I think it's exciting for Formula 1," Hamilton told Sky F1 at Mugello.
"It's quite a big shift from Ferrari to an up-and-coming team but I think Formula 1 really needs to keep the great driver that he is in the sport so I'm really happy that he's continuing and not stopping.
"I'm just really happy for him because it's not been the easiest of journeys at Ferrari, and I think he'll learn so much from there,
"I think it's one of the smartest moves that Aston Martin could do and I'm excited to see what he contributes and how he helps progress that team forward."
During the driver's press conference, Hamilton said he was convinced Vettel could end up at the team when he departs from Ferrari at the end of the year, but claimed it was ultimately the right decision moving to a team that are constantly improving.
"Honestly, I thought that was the ideal direction he was going to go, I thought it would happen," Hamilton added.
"I was really pleased to hear it because if you look at that team, it has new ownership, and has already taken a huge step forwards in its performance and it can continue to grow."
Bahrain International Circuit - Winter testing