The message will not be the only contact between the pair according to van Bronckhorst, who plans to quiz his predecessor after assuming the role at the Scottish champions.
The Dutchman reciprocated the well wishes to the new Aston Villa management team, but plans to speak to Gerrard about the squad and set-up he has inherited in the near future.
“He sent a message by email which was really nice and of course for him it's a change in club for him.
"I think we will definitely be in contact in the coming weeks to talk about stuff,” van Bronckhorst revealed on his first official appearance as Rangers manager.
"He has done a really great job at Rangers and now has moved to the Premier League to Aston Villa so I personally wish him all the best and there will be some contact in the next weeks.”
Van Bronckhorst will meet the playing staff tomorrow, two days after watching their Premier Sports Cup semi-final exit to Hibs at Hampden – however he has already sat down with club captain James Tavernier in the aftermath of the game.
“We had a meeting today with Tavernier,” van Bronckhorst added. “Of course he is the captain – he is an important player and an important member of the squad. I think the relationship between captain and coach has always to be a good one, not only with him but also with the squad.
"He is very influential as the captain and in the way Rangers play.”
Van Bronckhorst was carrying out his opening duties as the 17th permanent manager at Rangers including visiting the training ground and holding his first press conference before meeting the players on Tuesday.
“It was a good meeting [with Tavernier]. I saw other players who were at the training ground but I will meet with everyone tomorrow.”
Rangers also announced three members of van Bronckhorst’s backroom staff – Roy Makaay, Arno Phillips and Yori Bosschaart – will join him.