Anderson has agreed to terms on a multiyear contract to stay with the Browns, a person familiar with the negotiations told The Associated Press.
The person spoke on condition of anonymity because the contract had not been finalized.
General manager Phil Savage believed if Anderson had gotten an offer from another team, the Browns probably wouldn't have been able to keep him.
The Browns were prepared to turn their offense over to Brady Quinn.
The team had been negotiating a three-year, $20 million deal for Anderson.
The 24-year-old quarterback wasn't on the market for long, signing with Cleveland just hours after he became a restricted free agent.
The Browns also addressed their defensive needs by trading for a defensive lineman.
According to numerous reports, the team has agreed to a deal to acquire Green Bay's Corey Williams in exchange for Cleveland's second round pick in the 2008 draft.
Williams played tackle in the 4-3 scheme used by the Packers, but is expected to play end as part of the 3-4 defense for the Browns.
After sending this year's first round draft pick to Dallas in order to select Brady Quinn in 2007, this deal means the Browns currently do not have a pick on the draft's first day.