The change will be put to the F1 Commission and World Motor Sport Council to be rubber-stamped, bringing an end to a failed experiment to shake up starting grids with elimination qualifying.
The statement said FIA president Jean Todt and the sport's commercial supremo Bernie Ecclestone had accepted the move “in the interests of the Championship”.
The teams had earlier shown their unity in a letter to Ecclestone and Todt, calling for the 2015 system to be reinstated and rejecting an aggregate qualifying proposal put forward by the FIA.
With unanimity needed for any change to the 2016 regulations, the apparent impasse had threatened to ensure the unpopular new format continued in China for a third successive race unless one side backed down.
The 26-member F1 commission groups the 11 teams, commercial rights holder and governing body as well as other stakeholders.
This year's qualifying system, which saw drivers knocked out at timed intervals during the three sessions, was approved hurriedly before the start of the season to add excitement.
SOCIAL MEDIA BACKLASH
However, drivers were eliminated while sitting in the garages in the final stage rather than battling for pole on track as in the past, triggering a backlash on social media.
Todt and Ecclestone had ruled out going back to the old system at a meeting with the teams in Bahrain last weekend.
Williams deputy-principal Claire Williams said then that both bosses believed “going back to 2015 would create more confusion than is necessary”.
Teams agreed at the Bahrain Grand Prix to vote by Thursday on a compromise solution, which would have seen each driver do at least two laps in each of the three phases of qualifying with the times aggregated.
The argument was about more than finding the best way to line up 22 cars on the starting grid, however.
In a sport that can crunch vast amounts of data in milliseconds, it comes down to power and who really calls the shots, the teams or the FIA and Ecclestone.
World champions Mercedes and Ferrari supply eight of the 11 teams, giving them more muscle in decision-making.
“The FIA should write the regulations and say 'these are the regulations. If you want to enter the championship you enter. If you don't, don't,” Ecclestone told reporters in Bahrain.
He said the change to the elimination qualifying format came at the request of promoters, keen for more action during the early phases of the Saturday session, and a desire to shake up the starting grid.
Dominant Mercedes have won 34 of the last 40 grands prix and eight in a row.
Original source: F1 returns to old qualifying format