Courts replaces Kelly Tolhurst, who has moved to a new ministerial role within the Ministry of Housing, Communities and Local Government.
He will be responsible for matters concerning aviation, maritime issues, and security and civil contingencies.
Tolhurst, meanwhile, has been given a brief covering homelessness and rough sleeping, supported housing, domestic abuse and climate change, among other responsibilities.
She served as parliamentary under secretary of state at the Department for Transport, as aviation minister, from 13 February to 8 September.
In her relatively brief period in post, Tolhurst appeared before the government’s transport committee in late-May and was quizzed on the refund situation within travel, most notably on issues relating to airline refunds – but also refund credit notes.
The reshuffle was prompted by regional growth and local government minister Simon Clarke standing down.
Tolhurst’s successor Courts holds the seat of former prime minister David Cameron in Witney and West Oxfordshire.
He was previously a parliamentary private secretary to transport minister Shapps.