Negotiations between the Koreans - who are joint top of the K League 1 table - and Glory lasted barely a week before an undisclosed fee was agreed on Wednesday.
Davidson saluted Glory for allowing him to accept the lucrative move to one of Asia’s powerhouse leagues.
“When I came to the club I wanted to give myself the best opportunity to be successful, and Tony Popovic and everybody at the club gave me that platform,” he told The World Game.
“I’m very grateful for that - but in football when opportunities arise like this you need to grab them with both hands.
“Ulsan are a big club and are everything that Perth - having qualified for the (AFC) Champions League - are striving to follow.
“Ulsan are up there fighting for the title and play Urawa Reds tonight (Wednesday) chasing a place in the last eight of the ACL.
“To be a able to be a part of something like that - if the deal all goes forward - really attracted me.”
The approach for Davidson - who recently signed a season-long extension with Perth - came out of left field, quite literally.
The two-time K1 winners - and seven-time runners up - were initially looking for a winger and sent scouts to watch Adelaide United’s Craig Goodwin and Davidson’s Glory teammate Chris Ikonomidis.
Whilst Goodwin turned down overtures, flying wing-back Davidson caught the eye.
Coach Kim Do-hoon followed up by having him watched on several other occasions - with each trip only hardening his resolve to land the 27-year-old.
“If you perform on the pitch you just never know who’s watching,” added Davidson.
“For me, I was fortunate enough that they were watching our games and I played to a standard that interested them.
“They continued to watch and obviously they have come in and put an offer down which Perth have accepted.
“That showed how keen they were to bring me in mid-season, which was a huge positive.
“It’s a big reason why I was so interested in the move when I heard about it, because they just wanted to bring me in and they made it happen.”
Not yet able to force his way into Graham Arnold’s Socceroos plans, the 2014 FIFA World Cup player and 2015 AFC Asian Cup winner hopes this latest move can only strengthen his claims.
“Having an opportunity like this, to be able to go over there to a big club, and hopefully play week-in week-out will give me a stronger claim to the national team,” he added.
“For me now is just the beginning. It’s back to the drawing board.
“I must go over there and perform and get the job done like I did when I came to Perth. The hard work begins now.
“I’m feeling the best I have ever - strong, fit and slim.
“I’m coming off a holiday and while I aim to hit the ground running, it’s mid season and it may take me a little bit of time and the club understand that.
"I’m excited and hungry to go over there and prove a point, and have a real go at it.”
Having the played in the Netherlands' Eredivisie, England's Premier League and Championship - as well as in Portugal, Croatia and Slovenia - Davidson sees Asia as his next great frontier.
“I’ve been fortunate to have played a long time overseas,” he added.
“To come back to Australia and after just one season to win a Premiers Plate, make it to a grand final and get the opportunity to go overseas straight away is a blessing and something I don’t take lightly.”