The 28-year-old, whose last A-League experience came at the Wellington Phoenix, endured a frustrating wait for paperwork to clear on his move from Saudi Arabian club Al-Nasr.
"The last week to 10 days have been a bit frustrating but I knew there would be an end, it wasn't something we were fighting against, it was just a process we had to go through," McKain said.
"Once we cleared all of that it was a pretty straightforward process and quite an easy decision for me.
"There were a couple of options to explore but I was looking to come back to Australia and once I spoke to Rini and (director of football) Michael (Petrillo) about the plans for the team and what they want to do this season for the future of Adelaide, it was an easy decision.
"Seeing the squad Adelaide have got together here is something I'm excited to be part of and more importantly it's something I want to be part of."
McKain's signature follows that of Socceroo team-mates Dario Vidosic and striker Bruce Djite.
Coolen believes the arrival of the versatile McKain, who has 16 international caps, was vital after the departures of defenders Iain Fyfe and Robert Cornthwaite .
"Jon was already on our radar for a number of months. It's fantastic we can fit him in our squad, first of all because he's an Australian player with a lot of experience and leadership that we need," Coolen said.
"He is also an excellent communicator on the field, that's what we were looking for because we lost several defenders last season, so finding out that Jon was available was fantastic.
"He's 28 so it's a good period in his life, he wants to bring some stability into his life and settle in Adelaide for three years with his family."
Prior to his time in the Middle East, McKain - who began his career with Brisbane Strikers - spent two seasons in Wellington, which followed a stint with Romanian sides Politehnica Timisoara and National Bucharest.