An indicative vote this week gave the green light to the proposal by an 11-5 majority.
It would see the Old Firm clubs pay £25,000 each for the one-season arrangement.
The move has come in for considerable criticism from a variety of quarters, including the South of Scotland League.
A club statement said: “We would like to confirm that Dalbeattie Star voted against the introduction of Celtic and Rangers colt teams into the Lowland League for season 2021/22.
"The club board members studied the proposals thoroughly but felt the right thing to do was to vote no.
“However, we do live in a democracy and totally respect and accept the final decision which was to accept the colt teams for one season only.”
Opposition voiced – page 31