“It never was about money,” Beckham said.
“It never was about a payday.
“It’s about being a legend. And I think that this is about our everyday lives.”
Beckham claimed his trade to Cleveland took him by surprise, but he claims it is now something he’s looking forward to.
“As it all settled in I’m very excited about this and I think it’s going to be one of the best things that ever happened to me in my life,” Beckham added.
“At the end of the day, I know where I’m at in life.
“I don’t need to be in New York. I don’t need to be in L.A. I can be in Sheboygan, Wisconsin. It doesn’t matter where I’m at.
“I’ve created this what I’ve called a legacy. It never really crossed my mind going to Cleveland and worrying about marketing or worrying about any of that.
“I care about football. I care about winning. I didn’t step into this game to be famous, that’s just what fell into my lap.”
Last season Beckham was a vocal critic of the Giants’ poor performance and most notably their quarterback Eli Manning.
New York finished bottom of the NFC East with a 5-11 record and ended their campaign on a three-game losing streak.
Beckham was involved in 12 games, where he made 77 receptions for 1,052 yards and scored six touchdowns.
Speaking at the first day of the Browns’ voluntary offseason workout program, Beckham revealed what had been discussed with his new team-mates.
“We talked about legendary, we talked about a legacy, we talked about gold jackets – that’s our conversations,” he said.
“We do this every single day.
“You come in, ask questions and we’re up here answering them, but I think this moment is going to be more iconic than we all realise right now.
“That’s obviously what we want the goal to be. We’ll look back in ten years, ‘Man, remember April 1, 2019?’ The start of something great and I was happy to be part of that.”