The defender put pen to paper earlier this week - a welcome boost for the 27-year-old as he recovers after fracturing his collarbone against Chelsea on New Year’s Day.
He said, “It was a nice surprise to hear that the club were going to offer me a new contract after I’d picked up the injury because it shows that they have faith in me.
“This time last year I probably would have laughed if someone had told me how well things would go for me since the start of the season.
“I always believed I had the ability to play in the Premier League and I just needed a chance. I’m very grateful for the opportunity I’ve been given and want to keep working hard.”
Before suffering the injury, Burn had started all 21 Premier League matches for Graham Potter’s side.
The former Wigan Athletic man says that the trust shown in him by Albion’s head coach has had a positive impact on his performances so far this season.
“The boss has had the confidence in me to play me in a variety of positions, against some of the best wingers in the world," he said.
“It gives me a lot of belief going into matches. I’ve played under a lot of managers and I always try to take bits and pieces from all of them. Graham believes I can play with the ball and be a focal point from goal-kicks and so forth.
“I’ve not really played much as a left full-back as a professional, but I did play there quite a bit when I was younger. I didn’t think I’d be playing there in the Premier League, but I’m really happy with how it’s gone.
“I’ve had some tough matches and I just want to keep going, I love to learn and playing in the Premier League is what every child dreams of when they’re growing up, so I’ll play in any position I’m asked.”
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Burn is expected to be out of action until the beginning of March. He can now move his arm freely and says his rehabilitation is going well, but he can't wait to be playing again.
“Most injuries for footballers tend to be with your lower limbs," he added. “It’s just going to take a bit of getting used to and I have to take my rehab day by day, but I’m desperate to get back because I love playing and I’m missing it.”