The 24-year-old has joined United from Everton on a five-year contract for an initial £75m, with the deal believed to include £15m in add-ons.
Striker Lukaku said he and Pogba, who moved to Old Trafford from Juventus last year, are “always together”.
Speaking to MUTV, the Belgium international added that he had “the hunger to win trophies”.
Pogba, who has referred to himself as ‘Agent P’, last week posted pictures on social media of him and Lukaku together.
Lukaku said: “He is one of my best friends, and he is my neighbour as well. We are always together on a daily basis so he would explain to me how things were going.
“When he signed for United, to have witnessed that, it really triggered something in my brain and I knew that if one day I had the chance to sign then I would not say no.”
Analysis: Why £75m Lukaku is good move for Man Utd
Lukaku scored 25 Premier League goals for Everton last season, but in March said he did not “want to stay at the same level”.
Speaking on Monday, he said: “You just know and realise how big the club is, and the hunger it has to win trophies.
“I would like to say, at the end of my career, that I played for a team that has always challenged for trophies and this is what the club has always done.
To be here now is a blessing and I will not take this opportunity for granted.”
United boss Jose Mourinho was manager of Chelsea when they sold Lukaku to Everton for £28m in July 2014.
The striker spent the 2013-14 season on loan at Goodison before signing a five-year deal that summer.
Chelsea matched United’s offer to sign him from Everton, but Lukaku has been reunited with Mourinho.
“I am really looking forward to it, that is the most exciting part,” he said. “We have a really good relationship and I always dreamed to play under him since I was 10.
“To have the opportunity at 24 to work under him and to be part of his plans for challenges for trophies is exciting.
“I think he is a manager to help us to win trophies and I can’t wait to start working under him again.”
Lukaku has linked up with United on their pre-season tour of the United States, and trained with his new team-mates on Monday.
His move to the Red Devils means he will play alongside midfielder Marouane Fellaini for club and country.
Lukaku said: “He spoke to me two days ago and sent me a message saying: ‘Now you will discover how big and how great the club is.’ I said to him: ‘I have already realised it a little!’
“To have a guy who plays with me in the national team and one of my best friends in life in my team is great to get to know the players.”
Lukaku in stats
- With two goals against Hull City in March, Lukaku became the first Everton player since Gary Lineker in 1985-86 to score 20 league goals in a season.
- Lukaku is also only the fourth player to score more than 80 goals in the Premier League before turning 24 (after Michael Owen, Robbie Fowler and Rooney).
- He has scored more goals than any other Everton player in Premier League history (68).
- Lukaku is one of only three players to have scored more than 10 goals in each of the past five Premier League seasons (alongside Olivier Giroud and Sergio Aguero)