Irwin, 30, signed a two-year, $1.35 million contract ($675,000 average annual value). He has seven points (two goals, five assists) and 34 blocked shots in 31 games this season, his second with Nashville, and has 71 points (21 goals, 50 assists) in 260 games with the Boston Bruins, San Jose Sharks and Predators.
"It was a no-brainer," Irwin said. "Just looking at the opportunity they gave me last year to come up and re-establish myself at this level, I'll be forever thankful for that. When this opportunity came, it was a pretty easy decision."
Bitetto, 27, signed a one-year, $650,000 contract. He has three points (one goal, two assists) and 23 blocked shots in 22 games this season. Selected by Nashville in the sixth round (No. 168) of the 2010 NHL Draft, he has 16 points (two goals, 14 assists) in 86 NHL games.
"This is a championship team," Bitetto said. "It's a place I want to be, and it was a no-brainer for me to sign here. I'm excited for the opportunity to present itself."
The Predators defensemen have helped Nashville rank sixth in the NHL in goals-against per game (2.66) after reaching the Stanley Cup Final for the first time last season.
Roman Josi (2020-21), Mattias Ekholm (2021-22) and P.K. Subban (2021-22) are signed for at least the next three seasons. Ryan Ellis is signed through the 2019-20 season.
"We're pretty aware at how good we are as a group and how confident we are in here," Irwin said. "When we play the right way, we're a very hard group to beat. To be a part of that and go through what we went through last year and to experience that whole thing is something special. I'm really excited to be a part of this for a couple more years."
The Predators (24-11-6), three points behind the first-place Winnipeg Jets in the Central Division, host the Edmonton Oilers on Tuesday (8 p.m. ET; NBCSN, TVA Sports, SN1, SNE, SNO, NHL.TV).