A private indicative vote showed 11 clubs in favour, five against and one abstention after both Old Firm clubs made their case at a meeting with the league.
The decision will still need to be ratified at the league's annual general meeting on 27 May.
Here’s the latest details:
How much will Rangers and Celtic pay the Lowland League?
Full details of the deal are still to be made public but both clubs will pay £25,000 as entry payment into the league.
That £50,000 will be split between the existing clubs.
The Lowland League said work would take place "to make the required rule changes" for the plan to come to fruition.
Why do Rangers and Celtic want to enter B teams?
Rangers and Celtic believe giving their young players more exposure to senior football will help their development.
The two clubs’ Under-21 sides have competed in the Scottish Challenge Cup since 2018, along with counterparts from other Premiership clubs.
A recent proposal for Old Firm colts to play in a 16-team Scottish League 2 next season failed to attract support.
What is the Lowland League? What level is it at?
The Lowland and Highland Leagues are the fifth tier of Scottish football, with the champions of each division playing each other for the right to face League 2's bottom club in the League 2 play-off final.
Lowland champions Kelty Hearts face Brechin City in this month's two-legged final on 18 and 23 May. If Kelty win, they will be promoted to League 2.
The league has said that Rangers and Celtic won’t be eligible for promotion.
What have the Lowland League said?
Lowland League chairman George Fraser said: "Our league is fully committed to the integrity of the pyramid and we have shown this time and time again, so any suggestion we are not is ill-judged and misplaced.
"With all the tier six leagues opting to go 'null and void' this meant there was no champion club put forward to join the SLFL. If there was then the champion club would be taking part in the SLFL league next season."
What has Steven Gerrard said about Rangers B team?
Rangers manager Gerrard said: “I think it will be fantastic for everyone if people decide not just to think about themselves.
“If you’re thinking about the country and improving the Scottish national team at all levels, then what we want is to give the kids a better chance to develop into better players.
“If you can play against men earlier. If you can play for important points and give these kids more responsibility, put them in more pressurised situations with bigger crowds, I think that can only be for the benefit of the country.
“Obviously I’m sitting here as the Rangers manager (and people) will think, ‘You’re only saying that because you’re at Rangers and you’re being a bit selfish.’
“I understand those opinions as well but if I try to take myself out of the Rangers environment to answer the question and to think about the Scottish game and the national team, I think this is a big plus for Steve Clarke and any future national manager.
“A lot more Scottish kids will be getting challenged earlier playing men’s football, playing for points, playing in front of crowds. That brings your development on a lot quicker than playing games that have less significance and pressure.”