Raab, a former Brexit minister, was appointed by Prime Minister Boris Johnson earlier in the day as UK's foreign secretary and first secretary of state in a major cabinet reshuffle.
Raab told reporters after his appointment that Brexit process must be completed one way or another by the end of October, preferably with a deal.
Queen Elizabeth II accepted earlier in the day Theresa May's resignation from the post of prime minister and appointed Johnson, former London mayor and UK foreign secretary, as new head of the Cabinet.
Raab quit May's government in November 2018 over his disapproval of her compromise deal to leave the European Union.