The Scotland striker was introduced to the media - along with former Newcastle defender David Edgar - after completing his first training sessions as the temperature soared past a stamina-sapping 30 degrees Celsius.
And was instantly backed by Coyle to more than justify his hefty price tag.
"Steven will show he is worth more than that kind of money. He is a young man, an international and a proven goalscorer," Coyle said.
"He leads the line well, he can drop short and can play off the shoulder. He has such a range of assets and attributes.
"Steven is a very accomplished player for someone of such a young age and I am delighted he is here.
"Whatever price has been paid, the player didn't pay it. They just have to go and show the ability that brought them to this club."
Fletcher believes the move to Turf Moor and the Premier League will boosts his chances of a regular starting slot for Scotland.
He said: "I have been around the squad for a while now and hopefully I can get a few more games under my belt.
"But first of all I have to perform for Burnley and score goals. If I do that I will be delighted.
"There is a bit of pressure with the price tag but I will take it as it comes. It is important to get a good pre-season under my belt first of all."
Fletcher admitted it was a wrench to leave Easter Road.
"They gave me a great opportunity and I was there since I was 16,
" he said.
"I would like to thank everyone for all they have done for me. It was hard to leave but I wanted to play in the Premier League.
"As soon as I came to Burnley I knew this was the right move for me. Owen Coyle is very enthusiastic, he wants to play football the right way and there is a family feel about the place."
Hibs chief executive Scott Lindsay said: "Everyone here wishes Steven well in his career.
"He has been a terrific player for this club and we are sure he will go on to prove his worth in the top league in England."
Edgar will miss the opening Premier League game against Stoke after being sent off in Newcastle's final match when they lost 1-0 to Aston Villa.
He rejected a new deal and said: "It was horrible feeling that day and tough to be involved, especially as I have supported the club since I was a boy.
"Newcastle will always be in my heart and coming to Burnley is all about playing football, nothing else."