McGregor and Davis were both set to be free agents this summer with their previous contracts at the club expiring, before the duo penned new deals this summer.
The shot-stopper even snubbed interest from the Middle East to stay for one more year at Ibrox, while Davis also extended his stint for the same duration with boss Van Bronckhorst keen to keep them in his ranks.
Van Bronckhorst revealed that he was keen to not let McGregor and Davis leave the club this summer as they are important players both on the pitch and in the dressing room.
The Dutchman added that having players such as McGregor and Davis ensure his squad have a good balance of youth and experience which is a win-win situation for him.
Asked why he was so keen to tie down Davis and McGregor to new contracts, Van Bronckhorst told Rangers TV: “Well, I am really happy with them, with the performances.
“I think [It is very important] to have those players with experience in your team.
“They were both very important players in the locker room but still their playing abilities are there.
“So, I think that for me as a coach is a win-win situation.
“And I think we have a good mix in the team of experienced players, players who are coming into the prime of their careers and some exciting talents who will develop into important players for this club.”
Rangers are currently ramping up pre-season preparations in Portugal, while their recruitment department are working hard on making further signings in the transfer window, with Van Bronckhorst gearing up for his first full season in charge of the club.