Mackay won just five of his 24 league matches and his five-month tenure was ended on Monday after a 2-0 defeat to Derby County left Wigan eight points adrift of safety in the Championship with just five matches remaining.
Caldwell, who turns 33 on Sunday, comes as something of a surprise appointment as he has no prior coaching experience.
The centre-back has not featured for the club this term due to a persistent hip injury.
Caldwell, who won the FA Cup with Wigan in 2013 and two Scottish Premiership titles with Celtic, has been handed a permanent contract, but Wigan did not disclose the length of the deal.
Speaking to the club's official website, Caldwell said: "I've made no secret of the fact that I wanted to move into management when the time was right.
"I didn't expect that to come along as quickly as this but, in football, you need to take opportunities when they arise and I am honoured and excited in equal measures to take charge at the Latics, where I have shared such incredible memories over the past five years."
