Portadown, fifth in the Premier League last season, are not included because they missed the application deadline.
Armagh City and Limavady United's applications were not considered either because they did not have the required domestic licence.
Bangor finished third in the First Division last season.
They have not played at the top level since being relegated in 1995/96 when they finished last in the old eight-team division.
Clubs were assessed on league performances, attendances, facilities and provision for women's and youth football.
"We identified how much work needed to be done to get into the top 12," said Bangor chief executive Bill Peden.
"We concenrated on new facilities at our ground and getting the right personnel in place and now we have reaped the reward for that."
Final ranking of clubs
1 Linfield 1339 points
2 Ballymena United 1054
3 Glentoran 1016
4 Coleraine 965
5 Cliftonville 945
6 Dungannon Swifts 855
7 Glenavon 828
8 Crusaders 826
9 Lisburn Distillery 815
10 Newry City 796
11 Bangor 641
12 Institute 632
13 Donegal Celtic 543