The Church is the Body of Christ (consisting of both redeemed Jews and Gentiles). That precise definition is already in Scripture.
For as the [human] body is one, and hath many members, and all the members of that one body, being many, are one body: so also is Christ. For by one Spirit are we all baptized into one Body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit. For the Body is not one member, but many. (1 Cor 12:12-14)
According to this passage it is the Holy Spirit who baptizes or immerses every believer into the Body of Christ. That is also simultaneous with the baptism with the Holy Ghost, where Christ pours out the gift of the Holy Spirit to those who believe.