The cider brand name will be on Celtic's shirts for three years starting next season and Lawwell said the deal was worth more than the current sponsorship with Tennent's, which reportedly earns £1.5 million per year.
That deal is worth the same to Rangers but – unlike CR Smith, Carling and currently Tennent's – the Magners name will be on only Celtic's strips rather than those of both Old Firm clubs. Magners is owned by C&C Group which also owns Tennent's.
Some supporters had attempted to have a resolution passed at the annual general meeting in November which would commit the club to no longer entering joint sponsorship deals with Rangers.
The Hoops board refused to support that at the time, but yesterday Lawwell revealed that the partnership with Magners had already been agreed before that AGM took place.
"The deal was signed before the AGM so we knew we were doing it and we couldn't say so. They are different clubs with different values, histories, standards, traditions, different offerings I think in some ways.
"But in the past genuinely it was Martin Bain (the former Rangers chief executive) and myself who always set out on our own but circumstances always brought you back together because it was a local sponsor who needed both so you ended up back there."
Companies have been wary of sponsoring one Old Firm club, and not the other, for fear of alienating one huge set of supporters. Magners managing director Tom McCusker stressed that his company was still involved with Rangers.
He said: "We don't want to talk about Rangers, we are here to talk about Magners. We currently are involved with Rangers, because we are their shirt sponsors through the Tennent's brand.
"We started negotiations with Celtic quite a while ago. And it was always our aspiration to have a three-year agreement with Celtic to take them through their 125-year anniversary, which also coincided with the Tennent's 125-year anniversary.
"We are currently the shirt sponsors for Rangers and that will remain this season. Negotiations we have with them or anybody else are completely confidential and we can't talk about that."
Magners already sponsors the Magners League in rugby union as well as individual rugby league clubs and, previously in football, Dundee and Preston North End.
Meanwhile, Lawwell said he was unconcerned by criticism of league reconstruction by Rangers director of communications Jim Traynor, or by his suggestion that Celtic had been influential in forming opinion against them during last summer's votes on what should happen to the Ibrox club.
He said: "We're in a good place. We're not complacent but we're in a decent place at the moment and are going to look after our own business. These little things don't matter, really."
Some Celtic supporters wish to discontinue use of the phrase "Old Firm" because it binds the two clubs – some Rangers fans feel the same way – but Lawwell was uninterested.
"Again, we should leave it behind – not the Old Firm tag, but the whole subject – because there is positivity. Let's not go back into negativity and talk about other people's business. Let everyone get on with their own."
Lawwell claimed that, on balance, he did not miss Old Firm derbies.
"Not really," he claimed. "You miss the pluses and you don't miss the minuses. You miss the pros and not the cons, so it balances itself out. But you wouldn't swap it for the Champions League."
CELTIC have had only one expression of interest in a player since the January transfer window opened and manager Neil Lennon was under no pressure to sell, said Lawwell.
The priority was to look for possible additions to join new loan signing Rami Gershon – Central Coast Mariners midfielder Tom Rogic has arrived on trial – and also work towards a successful conclusion to negotiations on contract extension offers to Gary Hooper and Victor Wanyama.
Lawwell said: "I've had a call for one player, but it wasn't an offer, just a 'what's the story' call. Ideally I'd like a conclusion to the Hooper talks. Neil wants him to stay, we want him to stay. He has been a revelation here. Gary has the last 16 to keep him here. He has Celtic, he has everything that goes around Celtic.
"We would hope to hold on to him in January. We would hope to hold on to all our players in January and get to the last 16 of the Champions League (with the squad intact) because the manager wants it and that's what we will try and do.
"Neil wants to keep the squad together and if we can that's what we will do. If we can add to it we will add to it. But we have set down a strategy in terms of the type of player we want to bring in."
Celtic's friendly against Steaua Bucharest, during winter break training camp in Spain, will be shown live by ESPN on Tuesday, January 15, with a 6.30pm kick-off (UK time).