Ramsey, 28, will sign a two-year contract worth approximately $5 million, with about $1.5 million in guarantees.
The Houston Texans and Carolina Panthers also were interested in Ramsey, who recently was released by the New York Jets after only one season with the team. Ramsey will become the backup to Denver second-year pro Jay Cutler, and he ostensibly replaces Jake Plummer in that role.
Denver last weekend traded Plummer to Tampa Bay, and the veteran abruptly retired. The Broncos then began exploring their options for a proven veteran to back up Cutler, their first-round choice in 2006, and quickly targeted Ramsey.
The Broncos will be Ramsey's third team in three seasons, but one of the reasons he settled on Denver as his new home is the overall stability of the organization and the chance to settle in with a franchise and coaching staff he respects.
The first-round choice of the Washington Redskins in 2002, Ramsey has played in 34 games, and his résumé includes 24 starts. He has completed 480 of 862 passes for 5,649 yards, with 34 touchdown passes, 29 interceptions and a passer rating of 74.9. His best season came in 2002, when he made 11 starts for the Redskins. Although he had a 4-7 record that year, Ramsey had 14 touchdown passes and nine interceptions.
The former Tulane star threw only one pass for the Jets in 2006, and New York released him rather than pay a roster bonus due this spring.
Blessed with a strong arm and solid pocket presence, Ramsey has suffered from being overcoached at times and, certainly during his tenure under coach Joe Gibbs in Washington, he was mishandled and lost confidence.
Given the volume of teams that pursued him after the Jets released him, though, it appears there are still people in the league who value him.
Len Pasquarelli is a senior NFL writer for ESPN.com.