Gunter is returning to the Premier League following a previous spell at Tottenham.
McDermott is pleased with his latest acquisition and believes he epitomises the good work the club have done since promotion.
"I'm absolutely delighted that Chris has signed," he said.
"He was very, very keen to come to us and is another player who is young and very hungry.
"He's already played more than 200 games at club level, plus another 37 for his country, which is phenomenal for someone so young.
"Chris already knows our club well, he is very close to Garath McCleary, knows our Welsh players and I also know he met many of our squad over the summer too.
"With all the players we have brought in this summer they will improve and get better, and the most important thing is their hunger and desire.
"With all the business we've done this summer we think we've improved the quality in the squad considerably."