Nieuwenhuis was claimed off waivers by the Milwaukee Brewers on Wednesday to clear the 40-man roster spot for De Aza's addition.
Nieuwenhuis hit .208 with four homers and 13 RBIs in 106 at-bats with the Mets in 2015. He also appeared in 10 games with the Los Angeles Angels.
He originally was drafted by the Mets in the third round in 2008.
De Aza's signing became official Wednesday after he passed a physical.
Meanwhile, catcher Johnny Monell cleared waivers.