The Scottish Premier League and the Scottish Football League on Tuesday agreed in principle to a restructuring plan that would see the organisations merge in a 12-12-18 structure.
The proposals have not gone down well with Old Firm rivals Rangers but have been given the green-light by the Hoops.
Lawwell said: "We, as a club, support it. It's not perfect but it's the best available.
"I don't think you throw out the best in pursuit of the perfect.
"The big key here was that we had unanimity between the SPL clubs a few weeks ago, which was a major achievement and breakthrough in itself.
"I think it will be beneficial to the game, it will make sure there are more meaningful games and hopefully we will get more people through the turnstiles and more sponsorship."
He added: "We've got a meeting on the 28th.
"I'm a bit short on the detail which went on yesterday as I wasn't at the meeting. But, in principle, we are all in agreement.
"There will be a lot of detail to go through in the next two or three weeks but I've got great expectations that we will get there."
Asked if the new format could be in place for the start of next season, Lawwell said: "I think that's the plan.
"The plan would be, if it is achievable, and everything is agreed, it could go in from next year.
"But you don't want to rush anything if you're going to have a negative effect by getting it in sooner if it's not ready."
Lawwell - speaking as Celtic announced a three-year shirt sponsorship deal with Magners - refused to be drawn on Rangers' reaction to the plans.
A statement on the club's website, written by new director of communications James Traynor, yesterday described the reconstruction proposals as an "abomination".
Ibrox chief executive Charles Green has since claimed tonight that his Irn-Bru Third Division leaders should quit Scotland if the new format is rubber-stamped.
Lawwell said: "I don't want to talk about any other club's statements. There is a lot going on in Scottish football.
"We have just announced this fantastic deal, we are in the last 16 of the Champions League and we're going for three trophies."
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