The Dutch city was selected over Milan in November by the drawing of lots after three rounds of secret voting by EU states failed to produce a clear winner in the contest for one of the most prized spoils of Brexit.
The EMA must move from its current home in London when Britain leaves the EU next March, and Italy has launched a legal bid to overturn the choice of Amsterdam after it emerged the Dutch facility would not be ready on time.
The European Parliament on Thursday approved the relocation to Amsterdam but criticised the fact that "such an important decision" was taken by drawing lots.
Legislators also spoke out over how parliament -- the EU's only directly elected arm -- was shut out of the process.
"The European Parliament condemns the procedure followed for the selection of the new location of the seat, which has de facto deprived the European Parliament of its prerogatives since it was not effectively involved in the process," they said in a statement.
"The European Parliament insists that the procedure followed for the selection of a new location for the agencies will be revised and not used any more in this form in the future."
A delegation of MEPs who visited the site for the new HQ in Amsterdam last month said they were concerned the permanent building would not be ready by the target date of November 2019.
Temporary accommodation has been rented in Amsterdam to enable the EMA's relocation to begin on January 1, 2019, and be completed by March 30, 2019 -- the day the new post-Brexit era begins.
Based in London's Canary Wharf business district since 1995, the EMA evaluates and supervises medicines for human and animal use.
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