The match will take place at the Northern Commercials Stadium - kick off 7:45pm.
The winner of Tuesday's tie will play away to Burnley in the third round.
Admission prices will for the Boston match will be £3.00 for adults and £1.00 for all concessions (under 16s, over 60s, students).
Supporters will be able to pay on the turnstiles on the night. The lower tier of the JCT600 Main Stand will be open on an unreserved basis.
City's scholars booked their place in the second round thanks to a 1-0 home win over Hartlepool United at the start of the month.