Gotcha Day
n. The anniversary of the day on which a child was adopted.
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Besides providing him with a safe life, Bill and Judy did everything they could to teach Chris about Colombia. On ''Gotcha Day" — the day they received him from Colombia — his parents always gave him something from Colombia or Latin America. There were Colombian toys, books about Colombia, a visit to the UN Colombian delegate, even a special trip to see the Puerto Rico Day Parade in New York.
—Russell Contreras, “Seeking birth mom, he finds a cause,” The Boston Globe, December 25, 2005
They reach out empty arms. Children from another land move into them, and people who waited months or even years for these moments think, "Gotcha!"

That memory inspires many of these parents to informally celebrate "Gotcha Day" — the anniversary of their child's arrival, celebrated much like a second birthday.

But this year, Chicago's Spectrum Press, publishers of The Pumpkin Patch: A Single Woman's International Adoption Journey by Margaret L. Schwartz ($19.95), declared Sept. 15 as the first annual international Gotcha Day celebrating all adoptions, overseas and domestic.
—Sandra Pesmen, “'Gotcha' for good,” Chicago Sun-Times, August 29, 2005
1987 (earliest)
We've been a family exactly five years, yesterday being the fifth anniversary of the Daughter's arrival, her — our — Gotcha Day. She'd forgotten it was coming but understood immediately when she discerned streamers and balloons in the early-morning shadows. …

Rick and I have no precedents for a Gotcha-Day celebration, so it has been evolving slowly. The first year or two, we were just aware of this most important date, consciously grateful for our good fortune, for this daughter, for our family.
—Liz Aurbach, “Gotcha Day,” Christian Science Monitor, May 07, 1987
The Gotcha Day anniversary is also commonly called Adoption Day. Other choices are Family Day and Adoption Anniversary Day.