Daniel Sturridge opened the scoring with a sublime first-half strike after 32 minutes, before Gary Cahill and Phil Jagielka both converted Leighton Baines corners in the second half to give the hosts a positive send-off ahead of the World Cup.
It was England's final game at Wembley before they head to Brazil, but their next destination is now Miami where they will play friendlies against Ecuador and Honduras before their opening Group D fixture against Italy in Manaus on June 14.
The Three Lions have already completed a training camp in Portugal and Hodgson says that the win over Peru was the ideal way to continue their planning for Brazil.
"It is the perfect end to a perfect two weeks. It was a wonderful send-off to the World Cup by a quite incredible crowd.
"It didn't look as if it would be too comfortable in the first half, but as soon as Daniel scored that wonderful goal the game wasn't in doubt.
"To do it in front of 85,000 people was a great send-off, the atmosphere was a vote of confidence.
"When you play against teams with 10 men behind the ball you have to be patient but I had no doubt we would win."
Hodgson also confirmed that England had no injury worries after the game despite Leighton Baines being replaced by Everton team-mate John Stones in the second half with cramp.
"The most important thing for us was to come through it unscathed, injury-wise," he said.
"(Taking Baines off) was caution on our part. He could have continued but the game was over."
Speaking of absentees Luke Shaw, Alex Oxlade-Chamberlain and Phil Jones, Hodgson said: "They'll play on Wednesday (against Ecuador).
"They could have played tonight, but I determined they'd start the game on Tuesday and we had a lot of subs on the bench. We thought we'd give them another day's training."
Hodgson also defended striker Wayne Rooney who was replaced after 66 minutes following a frustrating display in front of goal.
"I was happy with Wayne Rooney's performance," he said.
"Rooney and (Steven) Gerrard are important members of our squad, and 3-0 seemed an opportunity to give younger ones a go. We think (Rooney's) fitness is progressing.
"I don't have any fears in that respect. His attitude and commitment are first class, even in a game of this nature. He has two more weeks to keep that going. I'm very pleased with the options I've got in my strike force."
Meanwhile, Peru boss Pablo Bengoechea, who hails from Uruguay, says there will be little to separate England and his countrymen when they meet on June 19.
He said: "I'd call it 50-50. They're two strong national teams, and it's a tough, difficult group full of strong sides.
"The key to it all will be the first set of matches. Get three points in the first game and it'll set you up nicely for the group stage.
"This was a warm-up game. I guess the England manager is reasonably satisfied with their performance, but the really tough stuff is still to come."