The midfielder was offered a new deal at the end of last season and put pen to paper at the Rams' Moor Farm training ground on Tuesday.
Bryson has been one of Derby's most consistent performers since joining the club from Kilmarnock in the summer of 2011.
"It's been an excellent two years here for me and, hopefully, the next three will be even better," said Bryson. "Derby gave me a chance to come down from Scotland and have a go at a higher level, so it was good to pay the gaffer and the club back.
"The club wants to move forward and be up there challenging - you can see that with the signings that have been made so far - and you can see what they are trying to build and I want to be a part of it.
"We want to improve on our 10th-place finish last season and try to get up into the play-off places - or automatic promotion spots. I don't see why we can't do that. We're stronger than we were last season and we've not lost too many players either.
"We weren't too far away last season and if we can maintain the same level of performance, there's no reason why we can't get there.
"But this league is so hard and every other team will be thinking the same thing. It's always the same - any team can beat any team so we know how tough every game is going to be."
Bryson was named player of the year in his first season at Derby and remained a key member of Nigel Clough's side last term, despite being hampered by a niggling groin injury.