Nomads, who finished as league runners-up in 2016-17, will host HJK Helsinki of Finland in the first qualifying round first leg at Bangor City's Nantporth.
Welsh Cup winners Bala will face FC Vaduz of Lichtenstein in their first leg ties at Rhyl's Belle Vue.
Bangor secured their place in Europe via the play-offs and they will be away to Danish side Lyngby BK.
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Bala Town will be appearing in the Europa League for the fourth time and hoping to reach the second qualifying round for the first time.
Manager Colin Caton says his side have learnt from previous campaigns, which included narrow aggregate defeats to Estonian side Levadia Tallin and Differdange of Luxembourg.
"Going into the first couple of seasons was going into the unknown really but we've got no excuses this time," Caton said.
"It's going to be a real tough test for us but we're going to give the best account we can."
Their opponents, FC Vaduz, qualified as Liechtenstein Football Cup winners but play in the Swiss leagues and were relegated from the Super League in 2016-17.
"People say that we've got the best draw and the easiest draw," Caton said.
"But we're playing against a team that's drawn with FC Basel - a Champions League qualifier - and beaten Young Boys."
Caton has added the experienced former Bangor City and Connah's Quay forward Les Davies and midfielder Eddie Toner to the squad which won the Welsh Cup in April.
And Caton says his side's 2-1 final victory over Welsh Premier champions New Saints will inspire the Lakesiders to achieve further success.
"There's still a massive buzz around the club," Caton told BBC Wales Sport.
"It's important that we all achieve again as a group and try and take it to the next step."
Connah's Quay Nomads manager Andy Morrison is under no illusions how tough a task his side face against Finnish side HJK Helsinki.
Morrison travelled to Finland to watch the Veikkausliga leaders secure their fifth successive victory with a 2-0 win over IFK Mariehamn last Thursday.
"It was an eye opener," the former Manchester City defender told BBC Wales Sport.
"I knew they would be good but they were better than I thought they would be. They should have won by many, many more.
"They're on fire at the moment. They're not conceding goals and creating a lot of opportunities.
"We've got an idea of how tough it's going to be but I've got all the faith in the world in the lads that they will give a great account of themselves."
Nomads have qualified for Europe for the second time having reached the Europa League second qualifying round last season.
Morrison says the games against Norwegian side Stabaek - whom they beat 1-0 on aggregate - and FK Vojvodina of Serbia will hold them in good stead.
They have prepared for Thursday's first leg with a 0-0 draw against Ballymena and a 2-0 defeat to St Johnstone and Morrison says playing a side who are midway through their season will be tough.
"The preparations are always difficult for a part-time club," Morrison added.
"I'm going to have lads coming off the beach and off their holidays on Wednesday night and then playing on Thursday.
"That's far from ideal but that's the football world in a part-time league.
"But there's a huge upside because it's a great experience."
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Bangor's play-off win over Cardiff Met in May secured European football for the first time in three years.
The Citizens have been drawn against Lyngby BK, with the first leg taking place in Denmark.
Kevin Nicholson, who was named the club's manager in May, is well aware of Bangor's proud European history which includes encounters against Napoli and Atletico Madrid.
"As a group there's a lot of excitement about being in Europe again," Nicholson said.
"It's obviously really important for Bangor City to be in Europe.
"Everybody at the club, the players, staff, and Gary Taylor-Fletcher as the caretaker manager at the end of last season, achieved that opportunity for the club and worked very hard to do that.
"What we are all aiming to do in these games against Lyngby is to make the most of the opportunity that the club has created for itself."
Nicholson hopes Bangor will not have to wait another three years to reach Europe once again.
"It is something we want to be involved in on a regular basis," he added.
"We're not just excited about these European games - were also excited about the league campaign coming up in August.
"Our aim is to qualify automatically for Europe through the league."
Live commentary of Bala Town v FC Vaduz & Connah's Quay Nomads v HJK Helsinki will on the BBC Wales Sport website.
Welsh Premier League sides Connah's Quay Nomads, Bala Town and Bangor City begin their Europa League campaigns on Thursday.