The renamed BAR team said in a statement on Tuesday that the 26-year-old, who joined in 2001, had signed up for another year.
Davidson will drive Honda's third car in Friday practice at grand prix weekends and stand in for Briton Jenson Button or Brazilian Rubens Barrichello should either be unable to race.
"To retain a driver of Anthony's calibre will greatly strengthen the team's performance and its ambitions of winning the constructors' championship," Honda Racing F1 said in the statement.
The driver had been linked to a race seat at Honda-powered Super Aguri, who are expected to get official approval to enter the championship later this week once a $48million bond has been paid to the governing body.
Davidson said he was looking forward to continuing with Honda.
"My decision to remain with Honda is the right one, for sure," he said in the statement. "They are committed to F1 for the long-term and absolutely focused on winning the world championship.
"Although I would prefer to be in a race seat in 2006, I am in the best possible position to work towards achieving that goal," he added.
Honda's Brazilian sporting director Gil de Ferran was confident Davidson would achieve his ambition.
"Although we all know that Anthony aspires to be a Formula One race driver, and we are all confident that this will happen eventually, his role at Honda Racing is crucial to us this season," he said.