Several Biblical personalities were adopted or were praised for adopting a child. These include:
- Osnas bas Poti Fera, who was married to Yosef, was adopted by Potifar/Poti Fera and his wife, and she was the daughter of Dina from Sh'chem (Tosfos al Hatorah to Breishis 41:45). Because Poti Fera adopted her she was called bas Poti Fera.
- Bilha was represented in Yosef's dream as his mother because she raised him after Rachel died (see Rashi, Breishis 37:10).
- Serach bas Asher was Asher's wife's daughter, but he fully adopted her. See Ramban & Yonasan ben Uziel, Bamidbar 26:46. (Daas Zekanim there has a lot of difficulty with that explanation. And see Haksav Vehakabala, Breishis 46:17. Tosfos, Pesachim 54a s.v. Eileh argues on the Ramban and says that one may not call his wife's son his son.)
- I heard that Yair ben Menashe was adopted by someone from Menashe, but he really was from shevet Yehudah (based on ibn Ezra, Bamidbar 32:41), but this is not conclusive.
- Moshe Rabbeinu was raised by Basya bas Paroh after she found him floating in the river.
- Esther was adopted by her uncle Mordechai after her parents died (Megilla 13a).
Does one fulfill perya verivya (procreation) by adopting a child? Most poskim say no. However a very famous R' Shlomo Kulger in Chachmas Shlomo (See Shulchan Aruch E"H 1) states: "I have had a doubt whether one who raises an orphan, if this is considered a fulfilment of perya verivya, since Chazal said whoever raises an orphan (boy or girl) in his home, the pasuk considers it as if he gave birth to them, if so one may suggest that it is like perya verivya, or, nevertheless, it's not like actually giving birth to the child. It seems to depend on an argument between Derisha and Taz on Y"D 242, that Drisha holds wherever the gemara says "ke'ilu" (as it does by adoption), the compared situation is not exactly identical to its analogy, and Taz argues and says they are exactly identical...." He continues to say to the Taz you do fulfill perya verivya and to Drisha you do not. But if you had children who died but you also adopted and raised orphans, even according to Drisha you will have fulfilled perya verivya - even though they weren't the same children, you did give birth to children and you did raise orphans.
Even if one may not fulfill perya verivya, it still is a very meritorious and wonderful thing to adopt orphans. See, for example, Pischei Teshuva, E"H 154:27 when discussing a couple that had been infertile for 10 years, must the husband divorce his wife, even though she was such a great wife, and one of her praises was that she allowed her husband to raise an orphan and learn with him. (The answer there was that he didn't have to divorce her, but that's not our issue.)