The signings of Smith, fellow second-rounder Darcel McBath, fourth-rounder David Bruton and sixth-rounder Tom Brandstater left the Broncos with just two of their 10 picks unsigned: Georgia running back Knowshon Moreno and Tennessee pass-rusher Robert Ayers.
Moreno and Ayers were both first-round draft picks.
Bruton is a free safety from Notre Dame, and McBath a free safety from Texas Tech. Brandstater is a quarterback from Fresno State.
Smith's agent, Drew Rosenhaus, said it was a priority to get him into camp on time.
"That was important to us," he said. "It's not easy when you have as many picks in the first and second round [as the Broncos have]. But they found a way to be creative. Alphonso's very happy."
Ayers was selected at No. 18 to help revamp a disappointing defense that surrendered 448 points in 2008. With the Broncos switching to a 3-4 scheme, Ayers will play more of a hybrid role as he alternates between the line and linebacker. He was primarily a defensive end at Tennessee.
The Broncos traded their No. 1 pick in the 2010 draft to the Seattle Seahawks to acquire Smith's rights.
Twelve second-round draft picks have made agreements. On Sunday, the Browns reached a four-year deal with defensive end David Veikune, the 52nd pick in the draft, and the Bills signed offensive guard Andy Levitre to a four-year contract.
John Clayton is a senior NFL writer for ESPN.com. Information from The Associated Press was used in this report.