Hewitt, who left the mercurial Kyrgios out of the tie against Bosnia and Herzegovina in February for "failing cultural standards", restored him to the side following the pair's heart-to-heart in America earlier this year.
Colombia and Belgium kick off the group on Monday (Tuesday 0300 AEDT) with Australia in action against the South Americans on Tuesday (Wednesday 0400 AEDT) before facing the Belgians on Wednesday (Thursday 0400 AEDT).
Hewitt believes Kyrgios is primed to shine in the Spanish capital after ending his season early to ensure he was in the best shape for the Davis Cup.
"We worked through a lot of things at the start of the year and then met up in Indian Wells in March," Hewitt said.
"Nick told me he was desperate to do whatever he could to get back in the team.
"One thing I have been really proud of with Nick is that he goes out of his way to help the rest of the boys week in, week out.
"Whether it be on the practice court or going to dinner. As an Australian it's pretty lonely out there on tour.
"You're away from home for a lot of months throughout the year.
"He's been really good in that capacity and he has been really good with whatever I have asked him to do leading into this tie.
"He had a slight injury and stopped his season early in Asia, and I think at the end of the day, his mindset was ready for this event and he is ready to go."
Australian No.1 de Minaur enjoyed a superb finish to the season that saw him win the Zhuhai Championships in September and follow that up by reaching the deciders of the Swiss Indoors, the Paris Masters and the ATP Next Gen Finals.
World No. 64 Thompson also has had a good year, bouncing back from a wretched 2018 season that saw him drop out of the top 100.
Former US Open quarter-finalist Millman and doubles specialist Peers, who won the 2017 Australian Open final with Finland's Henri Kontinen, make up a team that Hewitt believes is the most talented he's had since taking on the captaincy in 2015.
"On paper it probably is the best, but paper doesn't play," he said.
"The Davis Cup requires a different nerve and rankings get thrown out of the door.
"You need guys that are going to handle the pressure and expectation of playing for their country.
"But I have full belief in my five guys. I am very confident, very happy and know they are going to go out there and play bloody well."