Speaking after hosting talks in Brussels between Serbian President Aleksandar Vucic and Kosovo Prime Minister Albin Kurti, Borrell said the leaders agreed "no further discussions" are needed on the deal between the former wartime foes.
But Serbia still regards Kosovo as a breakaway province and flare-ups between the Balkan neighbours have stoked fears of a return to conflict.
Under the new deal, Serbia stops short of recognising Kosovo as an independent state but agrees to recognise official documents such as passports, diplomas and licence plates and not to block Kosovo's membership of any international organisation.
Borrell said the annex was an "integral part" of the new deal but it had not yet been agreed.
Vucic has insisted Kosovo establish an association of Serb-majority municipalities, as agreed by a previous Kosovo government.