New UK Prime Minister Liz Truss, who formally took office on Tuesday, has vowed to tackle economic challenges, but admits that it will not be easy.

Truss took over from Boris Johnson on Tuesday after she emerged victorious in an internal Conservative Party contest following Johnson's resignation in July.

"I am confident that together we can ride out the storm. We can rebuild our economy, and we can become the modern brilliant Britain that I know we can be," she said outside her new Downing Street home and office.

"I know that we have what it takes to tackle those challenges. Of course, it won't be easy, but we can do it," she added.

Truss was formally appointed by Queen Elizabeth II at a castle in Scotland during a ceremony on Tuesday. 

The 47-year-old former foreign secretary becomes the third female Prime Minister in British history after Margaret Thatcher and Theresa May.

(With input from agencies)