Fletcher has secured a four-year deal at Turf Moor following his £3million move from Hibernian.
Fletcher: "I have wanted to come to England for a while now to show people what I can do - and I am so looking forward to it.
"I want to give 100 per cent and score goals - and I hope I can do that.
"I am absolutely delighted to sign for the club.
"It is a great feeling to be here, and I am just looking forward to getting the season started now.
"As soon as I heard that Burnley were after me, and knowing Owen Coyle as I do from my time in Scotland, I thought this was the right place to come and develop my career.
"The opportunity came along in January for me to join Celtic, but Hibs did not think it was the right time to move on.
"When the chance arrived to come to the Premier League and play for a club like Burnley, I was glad they accepted that."