Wigan, who won the FA Cup and were relegated from the Premier League in 2013, are 23rd in the second tier - eight points from safety with five games remaining.
Caldwell, who played 111 games for Wigan but retired earlier this season because of a persistent hip injury, replaces Malky Mackay as manager following the Scot's dismissal on Monday after a 2-0 home defeat by Derby County.
The 23-year-old Sharpe, who took over as Wigan chairman from his grandfather Dave Whelan last month, said he did not consult his predecessor in sacking Mackay and appointing Caldwell.
"My granddad is over in Barbados, he didn't know what I was doing," Sharpe told a news conference. "I spoke to him afterwards and he was fully behind me. It will be a miracle if we stay up. I won't be judging Gary on the next five weeks.
"Gary is one of us. As soon as he stepped into coaching we could see how much potential he had, managing our club was something we could always see in him."
The 32-year-old Caldwell is Wigan's third manager of the season after Uwe Rosler was sacked in November before Mackay failed to halt the club's slide during his five-month reign.
Wigan, who were elected to the League in 1978, spent eight seasons in the Premier League between 2005 and 2013, and last played in the third tier 12 years ago.
(Reporting By Michael Hann, editing by Mike Collett)
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