Travis County District Judge Tim Sulak said actions by El Paso city officials to issue and obtain the bonds were "legal and valid," the El Paso (Texas) Times reported Thursday.
Sulak said objections raised by opponents of the bond issue did not "sufficiently show just cause."
The judge declined to rule on whether the city council should hold a May referendum to get voter approval for razing City Hall.
The ruling allows officials to proceed with plans to tear down the municipal building to build the stadium.
Sulak set a $1 million bond for an appeal of the ruling. Opponents have 30 days to file any appeal.
The city council last week approved placing a petition to save City Hall on the May 11 ballot. However, attorneys for the Triple-A Tucson Padres and the city say the wording of the petition would have little effect and not stop the demolition.