Burrows has featured 11 times for Posh this season, five in League One, and has picked up five assists in that time with three in League One and two in the EFL Trophy.
He has challenged experienced first-teamer Dan Butler for the position at left-back after impressing both supporters and Ferguson with his performances back in November and December when he replaced the injured Butler for three games.
Ferguson commented on Burrows' new deal, he said: "We feel he can play as a number 10 and off the right in a 4-2-3-1 formation, he understands the game and knows what we expect from him.
"He has areas of his game that he needs to improve on, but at 19, he has plenty of time to develop. I am really pleased that we have managed to get this done."
Burrows added: "I am really happy to get the deal over the line and really grateful to the club for putting their faith in me. I have been here a long time and the club means a lot, so to get to this point in committing my future long-term is really special.
"I have a couple of assists to my name this season, but obviously I know I need to add goals to my game. Wing-back is a role I really enjoy, I like the fact that you can be defending one minute and attacking the next and Dan Butler has helped me along the way because he has played a lot in that position.
"I can play in a few different positions, I played further forward as I was coming through the Academy, but I just enjoy being out there and playing first team football."
Goalkeeper Will Blackmore has signed a long-term professional deal with the club after becoming the latest graduate from Posh's academy.
Blackmore has featured regularly for under 18s and under 23s this season, while the19-year-old was on the bench in four EFL Trophy group stage ties earlier in the season.
Ferguson believes Blackmore has a bright future at the club and is pleased to have secured the services.
He said: "I am really pleased that we have been able to get it done. He has got a lot of potential and I believe he has a really bright future if he continues as he is. He has developed a lot over the course of the last 12 months and is putting pressure on the others to keep their standards high."
Blackmore is 'buzzing' to have secured a long-term future at Posh and is enjoying every minute learning under former Posh goalkeeper, and current coach, Mark Tyler, who believes the young goalkeeper has high potential.
Blackmore said: "I am absolutely buzzing! A lot of hard work has gone in to get me to this point, but I know there is a lot of hard work to come, but it is great to get to this point and let's see where it takes me.
"I am extremely grateful to the club for giving me this opportunity, I am really excited about the future and am enjoying every minute.
"It has been great working with Mark Tyler. He is a legend at this club and has helped me a lot, as have Christy and Dan, they have been great with me.
"I was actually an outfield player up until about the age of 14/15 so I am a bit of a latecomer to the party when it comes to goalkeeping, but I always loved making saves and obviously distribution is a big part of the position."
He could follow in the footsteps of Burrows, Ricky Jade-Jones and Flynn Clarke who have featured for first team since being graduated from the club's academy.