The pair commenced pre-season training at Murray Park on Monday and the club are delighted to have the prospects on board.
18-year-old Lang had been training with the club last season and has now signed up with the youth department, alongside 17-year-old striker Gibson, who arrives from England.
Head of Academy Craig Mulholland said: “I am pleased that both Tom and Jordan will be joining the Academy.
“They now have an opportunity to develop as footballers and people within the high performance environment we are creating within the Academy.
“Jordan was a good spot by our Academy scout in the Midlands, who also identified Kane Hemmings from a similar background a number of years ago.
“He is quick, has a trick and fits the new position specific player profile we are developing with the manager for all Rangers players.
“In addition to his footballing attributes he is hungry, desperate to be here and keen to learn and that is critical to the culture within the Academy.
“Like all young players he has many areas of his game he needs to work on and he will get the patience and support of the Academy staff to see what he can become.”
Lang is a Scotland international youth player, who plays in the same team as Gers striker Ryan Hardie and he came to Rangers after a spell with Birmingham City.
Mulholland said: “There was quite a bit of interest from several clubs in Tom before he decided to come to Rangers.
“He also fits the player profile model and importantly for a defender is a good user of the ball, which will be beneficial given the style of play throughout the Academy.
“A key part of our new style of play will be to dominate possession and therefore defenders who are comfortable in possession are important.
“He is also a good communicator and positive within the group which fits with the culture we are trying to create where it is vital that players are energisers and not energy sappers.
“We are delighted to have both boys on board, subject to their international clearance coming through, and wish them well in their career with the club.”