The Adventures of Tom Bombadil was written by J.R.R. Tolkien and published while he was still alive, and it is considered part of his Legendarium.
In universe, it is presented as a translation of some parts of the Red Book of Westmarch, the book where Bilbo and Frodo collected their writings.
It is a collection of short poems, mainly unrelated, rather than a real coherent prose narrative, so you can find it a bit different from other Tolkien writings, but it gives some background to Middle-earth.
It could be considered a florilegium of fairy tales and legends known throughout Middle-earth, especially being a part of Hobbit folklore, but there is nothing that can lead to think that it could be something like an "unofficial apocrypha".
About your question
Can I add this book to my Tolkien collection?
Well, this is really up to you; you can read and enjoy books regardless of their supposed "canonicity", it really depends on what you want to read and own.
Keep in mind that when talking about Tolkien, there is not such thing like an official canon with the same meaning used by modern so-called franchises like Star Wars, Star Trek, and so on, that also have many unofficial material produced by people other than the original creators.
Tolkien (and his heirs, but for different reasons) was extremely protective about his works, and everything that was written about Middle-earth comes from himself, there are no recognized "fan" writings with different level of "canonicity"; more or less whatever he wrote was part of his Legendarium; for what concerned him and his heirs, basically every derivative work that is not explicitly authorized (like the movies) is non existent.
Tolkien works are better classified as texts that are not equally finished and without a homogeneous status of their definitive versions, rather than being official or canonical.
You can get additional insights from this and this questions.