TNS, who won their 11th title in 2016-17, play the first leg at home on 27 June, with the return leg on 4 July.
In the Europa League, Bala Town face FC Vaduz (Liechtenstein), Connah's Quay Nomads have HJK Helsinki (Finland) and Bangor City play Lyngby BK (Denmark).
The first legs are scheduled for 29 June, with the return on 6 July.
Bala and the Nomads will have home advantage in the first leg, while Bangor will start away in Denmark.
If TNS beat Europa, they will face Croatian side HNK Rijeka in the Champions League second qualifying round.
But Saints interim manager Scott Ruscoe says they are keeping their minds on beating Europa FC first.
"It's not a bad draw logistically for us because it's going to be close with direct flights, things like that," said Ruscoe, who is in charge following Craig Harrison's departure to take over Hartlepool.
"I'm just pleased we didn't pick out the Armenian side or had to go to Kosovo, because that would have been difficult going into the unknown.
"We've seen enough of Europa FC, they're a decent side and... beat Lincoln to the title who were always thereabouts in [qualifying for] Europe."
Ruscoe revealed that the away leg on 4 July will be played in Portugal, possibly in Faro, as the pitch at the multi-sport Victoria Stadium in Gibraltar failed a Uefa inspection.
"A week Tuesday we'll be at Park Hall and after that in Portugal," he told BBC Wales Sport.
"We're very happy to be at home first, you can put your stamp on the tie early on.
"We're good at home. Touch wood, we can get off to a good start, we can suss them out... but our clear message will be to play our normal way."
Welsh Premier League champions The New Saints will face Gibraltar side Europa FC in the Champions League first qualifying round.