It was a busy day for the Lions, who earlier re-signed free agent cornerback Chris Houston and signed defensive lineman Jason Jones, formerly of the Seattle Seahawks.
The 28-year-old Bush showed the last two years in Miami that he can be an every-down tailback in Miami, rushing for 2,072 yards and 12 touchdowns in two seasons with the Dolphins.
Bush, who was used in a utility role in six seasons with New Orleans earlier in his career, played in every game last year for the first time since 2006 and finished with 986 yards, barely missing a second straight 1,000-yard season.
In 91 games during his career with the Saints and Dolphins, Bush has 4,162 yards rushing and 2,730 receiving, with 48 touchdowns, 29 rushing, 15 receiving and four on returns.
Reggie Bush with the New Orleans Saints