Adams has made a big impact since joining Leeds last summer and wasted little time in cementing himself in the starting eleven.
The 23-year-old is also leading the American side in the World Cup in Qatar despite there being more senior players in the US squad.
US head coach Gregg Berhalter left it to the players to choose the captain and Kljestan admitted that it was not a surprise for him to see his former team-mate emerging as the leader inside the dressing room.
The midfielder stressed that the Leeds star is a natural-born leader and was different from the players who he saw growing up.
Kljestan insisted that Adams was sure about his game and exuded confidence even when he was a youngster and looked and acted as a leader.
“Considering [the captaincy] was left to the players to decide, I’m not surprised it went his way”, the former New York Red Bulls star told The Athletic.
“I’ve known him since he was about 16 and I had him down as a natural-born leader very early on.
“It shines through in the way he is and the way he plays, this ultra-confident guy who kind of shocks you a bit but then quickly earns your respect.
“I was 20 years old when I became a pro and I was one of those players who always deferred to the older guys. Always. It’s what most players do.
“Tyler was nothing like that.
“He came through at 15, 16 and from day one, he was sure of himself, never the sort to keep his mouth shut if he had something to say.
“He speaks well, he plays well and that makes him an ideal captain.”
Adams’ United States will take the field at the Al Bayt Stadium in Qatar to take on England in their second Group B game tonight.
