Merrick told players of his decision after Sunday's 2-0 loss to Adelaide United left them bottom of the table with two wins and six losses from eight games this A-League season.
With a run of home games looming, beginning on Saturday against Central Coast in Hamilton, Merrick said the time was right for him to step aside.
"I think this will give my successor the best opportunity to take the team forward," said the 63-year-old Merrick.
Assistant coach Chris Greenacre and goalkeeping coach Des Buckingham have been appointed joint head coaches until Merrick's replacement is found.
Greenacre, a former Phoenix striker, filled a similar role for five games after Ricki Herbert's resignation in 2012.
A statement from the Phoenix on Monday said a "thorough process" was underway to find a new head coach.
Wellington Phoenix chairman Rob Morrison and Merrick will front a media conference on Tuesday at midday in Wellington, with no comment available from the club before then.
Among the candidates for Merrick's job is Rudan, who has just completed a four-year stint at Sydney United culminating in their National Premier League title win.
He is currently assistant coach for Australia's under-20 side.
Auckland City coach Ramon Tribulietx, linked with Brisbane Roar ahead of the 2015/16 season, is also among the candidates.
Tribulietx is in Japan, as Auckland prepare for their Club World Cup playoff against Kashima Antlers on Thursday.
Former Phoenix assistant coach Luciano Trani, who has also spent time at Melbourne City, Brisbane Roar and Adelaide United, and foundation Phoenix captain Ross Aloisi - currently assistant coach at the Roar - are also in the mix.
Merrick said in a statement that he had taken the team as far as he could.
