Kosmina returned to Adelaide in a part-time capacity when Dutchman Rini Coolen was demoted to youth coach in December.
The inaugural coach of teh club, he had held the post from 2003 to 2007, before resigning just days after the Reds lost the 2007 A-League grand final to Melbourne Victory.
After the Reds confirmed the appointment via Twitter on Tuesday, chairman Greg Griffin revealed the club had only had eyes for Kosmina.
"We're very comfortable with Kossie and we did not speak to a single other coach," Griffin said in a statement.
"Despite all of the coaches CVs that have been thrown at us, not one has been spoken to because we had an arrangement with John that we would let him finish off the AFC Champions League and we've decided to bring this forward, it is the club's decision because quite frankly everything we'd hoped he achieve he has achieved.
"You can see the spirit, you can see the fact that this team plays for something, so no other coach was contemplated."With just one week of the A-League regular season remaining, the Reds can still finish bottom of the standings. But Kosmina has guided his side to two wins from as many matches in the 2012 AFC Champions League group stages, and is keen to ensure it is just the beginning of a new era for United.
"[We want] to start to become recognised as a force and a consistent force in the A-League and Australian football, and a club that players actually want to come to and want to be part of it… and also it has got to be a club where local kids can strive," said Kosmina - himself a local product.
"Whoever comes here next season needs to fit the mould in terms of the direction the club wants to take, rather than the club trying to fit the mould of the players… the great teams around the world have their own philosophy and players that go to those clubs fit that philosophy."