The first leg of the tie will take place in the St. Jakob-Park Stadium on November 6, with the return at St James’ Park on November 27.
In the first round Basel beat Turkish club Malatyaspor on the silver goal rule after winning the away leg 2-0 and trailing the home leg by the same score after 90 minutes.
However they have enjoyed a spectacular start to their domestic season winning their first 13 games and also had an impressive Champions League campaign last season with Celtic, Liverpool, Deportivo La Coruna and Juventus among the opponents they defeated.
The other clubs we could have drawn were Torpedo Moscow, Hearts, Teplice, Hajduk Split and Blackburn’s conquerors Genclerbirligi, but Sir Bobby believes we have been handed the hardest draw possible.
"I think we've got a tough draw. I was looking at the list of teams that we could be drawn against and that was the one I didn't want, to be honest,” he said.
"It saves an awkward journey. We could have gone into Moscow, we could have gone into Croatia, we could have gone into Turkey, so it saves that.
"But in terms of match standard, it's probably the toughest draw we could have got. 'They did well last year against Celtic and Liverpool and they're way ahead in the Swiss league at the moment.
"I think the record says they've played 13 and won all 13, so I think we have a tough match, but I think they have one as well."
But Basel vice-president Gigi Oeri believes that we are strong favourites.
"We are very happy to have drawn an English club but I think at the moment they are happier than us," she told UEFA’s official website.
"The boys are doing very well and I hope they will win the championship and the (Swiss) Cup."
Full UEFA Cup second round draw
Dinamo Zagreb v Dnipro
Borussia Dortmund v Sochaux
Man City v Groclin Dyskobolia
Barcelona v Panionios
Benfica v Molde
Slavia Prague v Levski Sofia
Rosenborg v Crvena Zvezda
Valencia v Maccabi Haifa
Spartak Moscow v Dinamo Bucuresti
Gaziantepspor v Lens
Brondby v Schalke
Aris Salonika v Perugia
FC Utrecht v Auxerre
Steaua Bucuresti v Liverpool
Valerenga v Wisla Krakow
PAOK Salonika v Debrecen
FC Copenhagen v Mallorca
Parma v Austria Vienna
Basel v Newcastle United
Hajduk Split v Roma
Genclerbirligi v Sporting
Torpedo Moscow v Villarreal
Feyenoord v FK Teplice
Bordeaux v Hearts