Coutinho signed a four-year deal following a £17million move from Barcelona, who agreed to reduce the £33m option to buy included in the original loan deal.
The 29-year-old has become the highest-paid player at Villa, though it is understood Barcelona will be entitled to a cut of any future transfer fee.
"I've only experienced one window at Villa but I remember sitting down with Lucas Digne in January and him saying: 'What's happening with Coutinho?'" said Gerrard.
"Players ask questions. They want to know who they are going to be playing with, and they want to play with good players.
"If we are going to achieve things, players want to know they are going to be doing it with other good players. That's the way it is.
"Philippe is still in his prime. When he came here he wasn't really match fit and it was always going to take time for him to settle but he will be a big player here in the coming years."
Gerrard also said: "To have him here full-time and settled, he'll go up another level because that feeling of knowing where he's going to be playing his football for the next four years will help him settle.
"He's a player that needs to feel wanted; he needs to feel support.
"Everyone has played a part - me, the coaching staff, all the support staff and, most importantly, the owners, Christian Purslow and Johan Lange have made him feel really special.
"That's where the decision's come from. He feels really happy here and it's fantastic that he wants to be part of this journey.
"We're very pleased with the news. I was aware a little bit before it was announced and I think it's fantastic news for everyone connected with the club, most importantly the supporters.
"The reaction has been very positive because you've seen over the last five months he's played very well. There's still loads left in him, in our opinion."
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