The 24-year-old defender, who denied claims he had failed a medical at Birmingham City, signed a two-year deal at Ibrox a week after a move from Wigan to Birmingham collapsed following his loan spell at St Andrews.
A Birmingham director announced the club had withdrawn their interest after a medical and Kiernan was angered with the way the situation was portrayed, insisting that the chance to work with Warburton again saw him call off the move.
The centre-back first worked with the new Rangers manager as a 12 year old in the Watford youth ranks and also played for him during a loan spell at Brentford.
Kiernan said: “I respect Birmingham as a club and the manager and everyone there. I completed my medical there, I went back to sign the day after. The paperwork wasn’t quite ready. During that time, the phone call came from here.
“I was a little bit disappointed that it turned sour and [people said] I failed a medical.
“I don’t want to comment on it too much but I never failed a medical. I completed everything that was asked of me. I’ve got the email confirmations from the club.
“I came here and passed a medical and I’m ready to go on Saturday. I played a lot of football last season in the Championship and my body feels good.”
The former Republic of Ireland international added: “I’ve known Mark for a few years now and he has been good to me. As soon as I got the call, as soon as he got the job, I wanted to come here and work for him and do well for him.”
Kiernan is confident Warburton will be a success at Ibrox. “You can see what he did at Brentford, took the club up to the Championship and came very close to maybe going up again,” said Kiernan, whose nine loan spells included a short stint at Kilmarnock.
“He is very intelligent, very personable as well. You can talk to him and throw your ideas at him, if you don’t agree with someone then he will maybe tweak it. I’ve got a lot of respect for him. He wants to play football and attract players that want to play football. I know it’s going to be tough, I don’t expect to walk over teams but as long as we are all working hard together then we will be fine.
“Our initial objective is to get back to the Premiership. After that there are the attractions of the Champions League or wherever it might be. It’s up to us now.
“That’s why I came here, I want to be part of that. I want to look back on my career and look back on what I achieved.”