The 53-year-old Bowden, who officiated in 84 Tests and 200 one-day internationals over 21 years, amused fans with his unorthodox signals, especially his trademark crooked finger with which he indicated dismissals.
Along with Bowden, Derek Walker and Phil Jones were also demoted, while former first-class players Shaun Haig and Chris Brown have been promoted to the international panel alongside Wayne Knights.
"It's a massive opportunity for the guys and they deserve it based on their umpiring performances over recent seasons," NZC match officials manager Sheldon Eden-Whaitiri said on the NZC website.
"We're delighted to see more former players coming through the umpiring system and hope it continues to be seen as an attractive pathway," he added.
Bowden was dropped from the International Cricket Council's (ICC) elite panel in 2013, returned in 2014, but was omitted again after umpiring the Test between the West Indies and England in May 2015 in Barbados.