The German lost his place on the F1 grid at the end of the 2011 season. That year Sutil was also involved in a nightclub fracas for which he later received an 18-month suspended sentence.
Hamilton had been present at the club on the night of Sutil's transgression, but did not appear in court to testify.
The Briton said he has tried to get in touch with Sutil, who he knows well after their time as team-mates in Formula 3, since the incident and had emailed him while travelling to Barcelona to congratulate him for winning a return to the sport.
"I've emailed him several times," Hamilton said.
"A while ago when I heard there was a potential that he would get the seat I said I would pray for him, that I really hoped he gets it, that he deserves it [and that] I hope to see him back in F1.
"And then I emailed him on the way here as soon as I found out and said congratulations, I'm really happy for him."
Hamilton said he was yet to talk to Sutil but would welcome the opportunity to do so.
"I haven't heard back from him but I'm sure at some stage we will get to talk," he added.
"I'm looking forward to seeing him; I haven't seen him for a while.
"I think it's a great opportunity for him, I really wish him all the best for the year.
"I [left a message saying] 'I hope you go out and prove to everyone that they made the right decision'."
- Sports & Recreation