The Browns, who finished 1-15 last season, are the first franchise to pick No. 1 overall in consecutive drafts since Cleveland picked first in 1999 (when the Browns returned to the NFL) and 2000.
Cleveland also has the dubious distinction of being the first NFL team with multiple seasons with at least 15 losses.
"Honestly, I could care less about the No. 1 overall pick," Browns coach Hue Jackson said Sunday when asked during the postgame press conference about having the top pick again. "I'm more so (concerned) about that locker room. Those guys fight their tail off for me. They work hard. They do everything I ask.
"Like I told them, my disappointment is I can't get them to winning. That's unfortunate. We're not making enough plays to do it. That's kind of where we are."
Jackson, who has the support of Cleveland owner Jimmy Haslam to return next season, is 1-30 as the Browns' coach since taking over in 2016. The record marks the worst start of a head-coaching tenure since the 1970 merger of the AFL and NFL.
In last year's draft, Cleveland took Texas A&M defensive end Myles Garrett with the first pick. Garrett has played in the past 10 games after missing the first four games because of a foot injury and another because of a concussion. He has 27 tackles and five sacks.