The races were due to take place on 12 April in Bahrain and 19 April in the Saudi Arabian city of Jeddah.
This announcement comes after mounting pressure on the sport to decide whether these races would go ahead.
Both countries are located among the Gulf states, which have been struck by Iran in retaliation for US-Israeli air strikes, and the Sakhir circuit in Bahrain is just 20 miles away from a US base that has already been the target of Iranian attacks.
Safety remains the paramount concern for Formula 1 and the FIA, with President and CEO of Formula 1, Stefano Domenicali, releasing the statement: "While this was a difficult decision to take, it is unfortunately the right one at this stage considering the current situation in the Middle East.
"I want to take this opportunity to thank the FIA as well as our incredible promoters for their support and total understanding as they were looking forward to hosting us with their usual energy and passion.
"We cannot wait to be back with them as soon as the circumstances allow us to do so."
The scheduled F2, F3 and F1 Academy rounds have also been cancelled for these locations.
Following pre-season testing in Bahrain, some team freight is already stuck in Bahrain. This decision has been key in preventing further cargo from being sent to Bahrain ahead of the Grand Prix weekend. Had this decision not been made sooner, such cargo could have also gotten stuck, which would have been detrimental to teams like Aston Martin, who are already facing severe shortages of spare parts.
Both races have not been replaced on the busy March-December calendar. The season will now run to 22 Grands Prix, instead of the originally scheduled 24.
Consideration was given to relocating the races to tracks in Portugal, Italy, or Turkey. Ultimately, it was not possible to organise a race at any of these locations, given the short time limit and low chance of securing a hosting fee.
Bahrain and Saudi Arabia pay two of the highest hosting fees, meaning that Formula 1 is set to take a commercial hit in excess of £100m following the cancellations.
These funds get split between the teams and Formula 1, with each party now expected to take a hit of tens of millions, depending on how the prize money is split at the end of the season.
With no races taking place during April, there will be a gap of five weeks between the third round in Japan on 29 March and the now fourth round in Miami on 3 May. The teams will seek to make further improvements to their cars during this gap, as they continue to adapt to the sport's new regulations.