The Church's doctrinal office also said trans people could be godparents at a baptism and witnesses at a wedding.
The move follows attempts by Pope Francis to make the Church more welcoming to LGBT people.
The Pope told one trans person in July that "even if we are sinners, he (God) draws near to help us".
The Vatican's updated stance comes after Brazilian Bishop JosÃ© Negri wrote to the Church's Dicastery of the Doctrine of the Faith with six questions regarding LGBT people and their participation in baptism and matrimony.
On Wednesday the department posted on its website three pages in response, which was signed by the dicastery's head - Argentine Cardinal VÃ­ctor Manuel FernÃ¡ndez - and with the approval of Pope Francis.
It states that a transgender person - including those who have undergone hormonal treatment and gender reassignment surgery - can receive baptism under the same conditions as other believers "if there are no situations in which there is a risk of generating public scandal or disorientation among the faithful".
The document also explores Bishop Negri's other questions, including whether trans people can be a godparent. It says that where an adult has undergone hormone treatment and gender reassignment surgery they may be a godfather or godmother.
But it goes on to state that priests have the discretion to refuse such a request if "there is a danger of scandal, undue legitimisation or disorientation in the educational sphere of the church community".
American Jesuit priest Fr James Martin, who is a supporter of LGBT rights,posted on X(formerly Twitter): "This is an important step forward in the Church seeing transgender people not only as people (in a Church where some say they don't really exist) but as Catholics."
While the document seems to set out clearly what the Church thinks in terms of trans people being baptised or acting as godparents, it is more nuanced on the other issues raised by Bishop Negri.
On the question of whether same-sex parents who adopt or use a surrogate mother could have a child baptised in the Church, the Vatican said a priest's decision would have to be based on the "well-founded hope that he or she would be educated in the Catholic religion".
There was a similarly nuanced response to a question whether a person in a same-sex relationship could be a godparent at a Church baptism. It said the person had to "lead a life that conforms to the faith".
The updated guidance to Catholic clergy follows a suggestion by the Pope last monththat same-sex couples could receive a blessing from a priest- saying such a request should be treated with "pastoral charity".
Francis added, however, that the Church still considered same-sex relationships "objectively sinful" and would not recognise same-sex marriage.
Transgender people can be baptised in the Catholic Church as long as doing so does not cause scandal or "confusion", the Vatican has announced.