The Spain international was lured from Barcelona earlier this summer and the Blues captain is confident he can fill the boots of the departed midfielder
The 36-year-old was allowed to leave the club this summer upon the expiration of his contract after agreeing a move to MLS side New York City.
Fabregas was subsequently signed from Barcelona on a five-year deal for a fee of around €38 million [£30m] and Terry is confident the Spaniard will be able to fill the boots of the club's all-time record goalscorer.
“He’s a very good signing,” Terry told the club's official magazine. “He is great on the ball, a great box-to-box player, he scores an awful lot of goals as well and he has got an aggressive streak in him too – I certainly remember that from his Arsenal days.
“I’m sure he is going to fit in really well at Chelsea and do well in the years to come.”
Lampard announced his decision to leave the club in June and Terry admits he was upset to see one of his closest friends - and Ashley Cole - depart Stamford Bridge.
“It feels different coming in and Lamps not being sat next to me,” he added.
“We have sat next to each other in the changing room since... well, since he signed for the club really. I’ve become really close to Lamps and Ash and they were my two best mates at the club.
“So I’m really sad to see arguably the best player the club has ever had, in Lamps, move on, for what he brought to the dressing room and as a mate.
“You understand that you all get older, but you just hope that point doesn’t come.”
Diego Costa and Filipe Luis have also been signed this summer to add to Fabregas' acquisition and Terry is confident heading into the new season, believing they can add another trophy to their ever-expanding cabinet.
“I think we should be very competitive,” he said. “We were close last year, but just unlucky at times.
"With the signings we have made and a couple of younger players who I think will surprise a few people this year, I think this should be a very good year.
"We want to win trophies – that is always the aim from the outset for me.
“I can see a lot more teams in the mix. First and foremost, though, we need to be solid, both home and away, because I think we dropped too many points against teams we shouldn’t have [last season]."