The first-round draw will come from the National Football Centre at St George's Park in front of a live audience on Monday, 27 October.
"We're delighted to bring back the tradition of the FA Cup draw on Mondays," said BBC Sport's Mark Cole.
"We hope the new early evening show will generate a great interest for our audiences on TV, radio and online."
Mark Chapman will present the coverage from 19:00-19:30 GMT on BBC Two and Radio 5 live, and you can also follow the draw on the BBC Sport website.
The new Monday evening draw is set to evoke memories of families huddled around the radio to listen to those all-important fixtures being announced.
FA Cup draws used to be very formal until about 15 years ago.
Two men in blazers would pick the teams from a velvet bag at Lancaster Gate, the Football Association's old headquarters in central London on Monday lunchtime and former FA chief executive Graham Kelly would announce the ties in his distinctive high-pitched tone live on radio.
This season, BBC Sport will take the FA Cup draws live on the road from different venues across the country throughout the season, including a few surprise locations.
Forty ties will be drawn in this first round, as 48 clubs from League One and League Two join the non-league teams who have battled their way through qualifying.
The Football Association's FA Cup media officer, Matt Phillips, said: "The draw at St George's Park is going to be a very special occasion and totally different to anything we've done before with a studio audience that will represent all levels of our national game.
"The FA Cup is a real adventure and we're delighted that the BBC will be there to tell the story to football fans across the globe."
Audiences will be able to watch up to 16 live matches on BBC TV along with highlights and listen to all the action on Radio 5 live. In addition, every FA Cup goal will be available online at bbc.co.uk/sport across every device.
BBC Sport has a four-year FA Cup rights contract running until 2018 in partnership with BT Sport.