"We are of course very happy for this positive decision so early in the day," a post on the SwissTennis website read. "It will allow us to prepare for this playoff under the best of conditions."
The two Swiss stars won Switzerland's first Davis Cup crown last November when they defeated France in Lille.
But they missed the first round defeat against Belgium this year to concentrate on their play in the Grand Slam events, Wawrinka taking full advantage to win the French Open.
There was also the matter of qualification rights for next year's Rio Olympics with both players needing to play at least one Davis Cup tie before next summer to be eligible.
The winner of the tie from September 18th-20th in the week after the US Open will stay in the 16-strong World Group with the loser dropping down to the second tier.
SwissTennis said that a decision on where the match would be played in Switzerland would be taken at a later date.