Parker and Hodges were unveiled on Friday just over two hours after Thaiday revealed he'd decided to step down as captain under pressure from coach Anthony Griffin.
Thaiday, who captained the Broncos for the past two seasons following Darren Lockyer's retirement in 2011, was told by Griffin following Australia's World Cup campaign that the captaincy was affecting his playing form.
The Queensland and Australian front-rower says he fought to retain the role but had reluctantly accepted it was the best move for the club to step down.
"The coach's thoughts were that it would be best for myself, and the team, and I play my best football when I don't have the added responsibility of being the Broncos' captain," he said.
"I'm 100 per cent behind the team and what we're doing in the 2014 season ... this decision, even though it's probably one of the toughest ones I've had to make in my footballing career, has been made to benefit the team and, myself being a team man, I'm always trying to put the team first."
During Thaiday's two seasons as club captain, the Broncos snuck into the finals in eighth spot before finishing 12th - the worst finish in the club's 25-year history - last season.
Parker, 31, is coming off a brilliant 2013 when he regained a spot in the Queensland State of Origin team and earned a spot in Australia's World Cup-winning squad.
Hodges, also 31, is recovering from an achilles tendon injury and Parker says he is happy to share the role.
"One of Hodgo's greatest traits is he's got a lot of followers that want to follow us," he said.
"I think between the two of us, we'll do a good job."
Griffin said he had to deliver his thoughts to Thaiday in the best interests of the club.
"My role is not to always to tell people what they want to hear," he said.
"By not addressing what I see as a coach, I'm not helping the player. Sam's going to be a more consistent and relaxed player without those responsibilities."
Thaiday said he would remain committed to the Broncos despite losing the captaincy.
"This is my 11th season at the club," he said.
"I'm contracted here until 2015 and I have every intention to re-negotiate with the club and stay here.
"It's a decision that I've made and I'm looking forward to getting back to playing the best football I can."