A Broadway round of musical chairs is skedded for early next year, with Beatles tribute “Rain” set to shift from the Neil Simon Theater to the Brooks Atkinson, while current Atkinson tenant “Rock of Ages” jumps to the Helen Hayes.

The show now occupying the Hayes, Colin Quinn solo outing “Long Story Short,” has just extended its limited engagement to Feb. 5, when it’s now set to shutter.

The moves will extend the lives of two shows as Broadway heads into the traditionally rocky months of January and February, when sales slump in the post-holiday hangover.

Changing theaters is not uncommon on the Rialto, which has seen mid-run shifts for long-runners including “Chicago” and “Les Miserables.”

But whereas this usually involves a show moving to another theater owned by the same company, “Rock” will go from Nederlander’s Atkinson to the Hayes, a venue independently owned by partners Martin Markinson and Jeff Tick.

The Nederlander also owns the Simon, which is booked in the spring for the stage incarnation of “Catch Me if You Can.”

The theater switches were initiated by company execs James L. Nederlander and Nick Scandalios once the consistently rising advance sales for “Rain” caught their eye. “By about the third week of the run, you felt the wraps really beginning to propel themselves,” said Scandalios.

But since none of the company’s nine Main Stem venues are available this spring, a move to a theater outside of the Nederlander chain was necessary for “Rock” if “Rain” were to maintain its sales momentum via a run at the Atkinson.

The shifts allow “Rain” to extend what was initially set to be a 12-week engagement on Broadway. At about 1,000 seats, the Atkinson has about 450 fewer than the Simon.

Running costs for the show won’t be hugely different, accordingto “Rain” producer Lee Marshall. “It’s not much of a cost savings for us, but now I have a theater for the spring,” he said, adding the production recouped it capitalization costs over the weekend.

Since debuting in late October, “Rain” has posted an average attendance of about 65% of capacity — which, according to per-seat sales, would come close to 100% at the Atkinson. New run will open with a 16-week sked plus the potential for an additional extension.

According to “Rock” producers Matthew Weaver and Carl Levin, running costs for that tuner will go down substantially in the Hayes, which at less than 600 seats is the smallest venue on Broadway. “The main savings are the front-of-house costs and the rent,” Levin said.

A manageably low running cost is generally credited as a major factor in sustaining a long life on the boards. Weaver and Levin said they hope to keep “Rock” on Broadway for the next two to three years, looking forward to a potential profile boost that could come from a film version targeting a spring start and a 2012 release.

“Rock” has grossed about $45 million since it began Broadway perfs in March 2009. Last week the production posted about 64% attendance, which in terms of seats sold would fill the Hayes.

The owners of the Hayes are in the middle of selling the venue to Off Broadway nonprofit Second Stage Theater, but the completion of that sale remains a ways off yet.

Purchase is expected to be finalized in May 2012.

Exact start dates for the shows in their new theaters remain to be set, although Marshall said “Rain,” which now plays through Jan. 12, is likely to start at the Atkinson Feb. 8.

“Rock of Ages,” meanwhile, will finish its run at the Atkinson Jan. 9 with the aim of beginning perfs at the Hayes in March.