Baird, 33, who has 72 caps for his country, moves to County on a two-year deal, with the option of a further 12 months, after leaving West Bromwich Albion following one season
The Northern Irishman becomes Derby’s fifth summer signing, following the arrivals of Darren Bent, Alex Pearce, Scott Carson and Andreas Weimann.
Baird told the club website: “I’m delighted to be here and to be part of what is happening.
“The players the club have been bringing in so far have been top quality and that can only stand us in good stead for the season ahead.
“I have come here to help in any way that I can. It’s up to the Head Coach at the end of the day – whether it is the holding midfield role or anywhere across the back four – I just want to play football.
“I know that it is not going to be easy, but I’m going to work hard here and I hope that I will be able to play a lot of games.
“The leagues are very different, but everything about this club is geared up to be playing in the Premier League.
“With the new head coach, the club have been making Premier League signings and I’m in doubt that we are going to have a terrific season.
“I’m looking forward to coming in now in just over a week’s time and getting down to the hard work.
“I’ve done a few pre-seasons now. It’s an exciting time for the club and I’m looking forward to a successful season.”
Head coach Paul Clement said: “We’re very pleased to welcome a player of Chris Baird’s experience to Derby County.
“He is an excellent professional and he is an important addition for us, both on the pitch and also in the dressing room.
“This is another extremely positive signing for us and we’re very pleased with the business that we have conducted in the transfer market so far this summer.”
Baird played 24 times for West Brom in his only season at the Hawthorns to take his club appearances’ total beyond the 300 mark after spells at Southampton, Fulham, Reading and Burnley.