We present a general theory of braided quantum groups in the C*-algebraic framework using the language of multiplicative unitaries. Starting with a manageable multiplicative unitary in the representation category of the quantum codouble of a regular quantum group $\mathbb{ G}$ we construct a braided C*-quantum group over $\mathbb{ G}$ as a C*-bialgebra in the monoidal category of the $\mathbb{ G}$-Yetter-Drinfeld C*-algebras. Furthermore, we establish the one to one correspondence between braided C*-quantum groups and C*-quantum groups with projection. Consequently, we generalise the bosonization construction for braided Hopf-algebras of Radford and Majid to braided C*-quantum groups. Several examples are discussed. In particular, we show that the complex quantum plane admits a the braided C*-quantum group structure over the circle group $\mathbb{ T}$ and identify its bosonization with the simplified quantum $E(2)$ group.
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