The 21-year-old defender made the loan move only after signing a new three-year contract with the West Yorkshire outfit, as reported by BBC Sport.
The youngster, who can operate as a right-back or as a right-winger, has revealed that the presence of Rosler was key in him choosing Fleetwood.
Rosler, who was in charge of Leeds from May 2015 until October 2015, was appointed the Fleetwood head coach in July 2016.
Under the 48-year-old former Wigan Athletic manager, the Fishermen finished fourth in League One during the 2016-17 campaign.
Fleetwood are ninth in the League One table at the moment with 19 points from 11 matches, just a point behind sixth-placed Charlton Athletic.
“He told me his thoughts for the season, I told him mine and it was obviously the right move for me,” Coyle told The Yorkshire Evening Post. “He was a massive factor in me coming here, him and Rob Kelly (Rosler’s assistant).
“I didn’t play under them at Leeds but I trained with the first team and I felt at the time that they brought me on leaps and bounds. I only had good things to say about them.
“I’m not sure of the exact stats but Fleetwood have had something like six promotions in 10 years. They’re an ambitious club and you feel that when you get here.”