Adoption in the sense of changing one’s identity and lineage for a false lineage is prohibited in Islam; but at the same time, it is allowed for Muslims to adopt a child in the sense of taking him/her under his/her wing for providing both physical and spiritual care for him/her. The Prophet (peace and blessings be upon him) said, “The best house of Muslims is one where an orphan is cared for.”
Sheik Yusuf Al-Qaradawi, stated in his well-known book, The Lawful and the Prohibited in Islam:
“The type of adoption which has been abolished by Islam is that kind which makes a boy a member of the family, with all the rights of inheritance, the permissibility of mixing freely with other members of the household, the prohibition of marriage and so on.
But the word “adoption” is also used in another sense, one which is not prohibited by Islam—that is, when a man brings home an orphan or a foundling to rear, to educate, and to treat as his own child (fostering); he protects, feeds, clothes, teaches, and loves the child as his own. However, he does not attribute the child to himself, nor does he give him the rights which the Shari`ah reserves for natural children. This is a meritorious act in Allah’s religion, and the man who does it will be rewarded by being admitted to Paradise. Said the Prophet (peace and blessings be upon him), “I, and the one who raises an orphan, will be like these two in the Garden,” and he pointed to his middle and index fingers with a slight gap between the two.
A foundling (laqeet) is regarded as an orphan (yateem), and one may also apply the term wayfarer (ibn as-sabeel), one of those who must also be cared for, to him as well. [The “Wayfarer” is one of several categories of people mentioned as deserving of charity in various Qur’anic verses, notably 2:176 and 9:60. A foundling or orphan can also be considered as belonging in this category and hence as doubly deserving of help and charity.]
If a man has no children of his own, and he wishes to benefit such a child from his wealth, he may give him whatever he wants during his lifetime and may also bequeath to him up to one-third of his inheritance before his death.”