Johnson, who was relegated with the Midlands club at the end of last season, replaces midfielder Karl Henry as captain after joining for a reported fee of £7m.
"I'm really pleased," the 28-year-old told Sky Sports. "Obviously I've only been here a couple of weeks so to be named captain....
"I'm enjoying it [at Wolves], the lads are superb."
Johnson made 76 appearances in two seasons at Birmingham, after joining from Cardiff for a fee of £5m.