The tournament for teams outside the top flight will also include an under-20s side from each Scottish Premiership club in the first round.
Four teams from the Highland League and four from the Lowland League will also enter at that stage in August.
Two Welsh sides and two from Northern Ireland enter the last 16 in October.
It is expected these will be the top two from the Welsh Premier League and Northern Ireland Football League, meaning places for The New Saints and Bala Town and Crusaders and Linfield.
One Welsh side and one from Northern Ireland will be guaranteed a home tie.
Draws will be regionalised throughout the competition and seeded for the first three rounds, with the final to be played in March.
"We are very pleased to be supported by Uefa in delivering an element of cross-border competition through the invitation to our colleagues in Northern Ireland and Wales," said Scottish Professional Football League chief executive Neil Doncaster.
The SPFL say the majority of fixtures will take place during international weekends, while BBC ALBA, S4C and Premier Sports will all show live matches.
Championship winners Rangers lifted the trophy last season, beating Peterhead in the final at Hampden.
Scottish Challenge Cup
Round 1 (August) - 28 teams: 12 x Premiership U-20 teams, 8 x League 2 teams, 4 x Highland League teams, 4 x Lowland League teams
Round 2 (August) - 24 teams: 14 x Round 1 winners, remaining 2 x League 2 teams, 8 x League 1 teams
Round 3 (September) - 24 teams: 12 x Round 2 winners, 10 x Championship teams, remaining 2 x League 1 teams
Round 4 (October) - 16 teams: 12 x Round 3 winners, 2 x Northern Ireland Football League teams, 2 x Welsh Premier League teams
Quarter-finals (November): 8 x winners from Round 4