Celtic will host Hearts in the second round of the Scottish League Cup while holders St Johnstone visit Arbroath.
Rangers have a home tie against Dunfermline and there's a repeat of last season's semi-final between Livingston and St Mirren.
Motherwell visit Dundee in an all-Premiership tie while Hibernian are at home to Kilmarnock.
Raith Rovers host Aberdeen and Dundee United visit Ayr United with the ties to be played on 14 and 15 August.
Promoted Hearts host Celtic in Saturday's Scottish Premiership opener, with the sides having last met in December's Scottish Cup final.
The 2020 showpiece had been delayed because of the Covid-19 pandemic and Celtic prevailed on penalties after a thrilling 3-3 draw.
"It's an excellent one for us," Neilson told BBC Radio Scotland's Sportsound. "You want to play against these teams and if you're going to progress and try and win cups then you have to beat these teams.
"It's important that we look at it positively because it is a great draw for us."
Livi edged out St Mirren 1-0 in last season's semi-finals before being beaten by the same scoreline in the final against the Perth Saints, who also won last season's Scottish Cup.
St Johnstone, like Scotland's other European representatives Aberdeen, Celtic, Hibs and Rangers, enter at the second round.
Ayr, Dundee, Dundee United, Hearts, Kilmarnock, Motherwell, Raith Rovers and St Mirren won their first-round groups while Arbroath, Dunfermline and Livingston progressed as the three best runners-up.
Rangers v Dunfermline
Arbroath v St Johnstone
Hibernian v Kilmarnock
Ayr United v Dundee United
Celtic v Heart of Midlothian
Raith Rovers v Aberdeen
Dundee v Motherwell
Livingston v St Mirren
Ties will be played on 14 and 15 August