He has also named MEP Mike Hookem, who had previously held the defence and veterans brief, as fisheries spokesman.
MEP Julia Reid gets the environment brief and party treasurer John Bickley will speak on immigration.
Mr Nuttall was named leader on Monday, having secured 62.6% of support among party members.
He also announced one of his defeated opponents - Suzanne Evans would become UKIP's co-deputy chairman, along with South West of England MEP William Dartmouth.
Paul Oakden will remain UKIP chairman and East of England MEP Patrick O'Flynn is the leader's principal political adviser, while former leader Nigel Farage has been offered the party's honorary presidency.
Mr Batten, an MEP for London, accused Prime Minister Theresa May of doing "nothing" since entering power in July to move Brexit along.
He said UKIP would "reject" having to invoke Article 50 of the Lisbon Treaty - which gets formal exit negotiations with the EU under way.
He added: "Rather, we will call for Parliament to repeal the European Communities Act (1972) immediately as the first step in the process. This will restore law-making supremacy to the UK Parliament and put the British government in the driving seat of negotiations, not the EU."
Mrs May has promised to trigger Article 50 by the end of next March, but Mr Batten said her strategy was to "delay and delay the whole process in order to fudge it".
Accepting his fisheries brief, Mr Hookem, an MEP for Yorkshire and the Humber, said: "Currently, the UK allows trawlers from across the EU to plunder Â£1.5bn of fish from our waters each year, and British boats have only 13% of the fishing quota in our seas.
"This plundering of our national wealth must stop. Brexit is our opportunity to reclaim our seas and revitalise an industry currently on its knees."
Mr Nuttall, an MEP since 2009, beat Suzanne Evans and John Rees-Evans in the UKIP leadership contest.
New UKIP leader Paul Nuttall is continuing to form his team, appointing MEP Gerard Batten as the party's spokesman on Brexit.