We study a general class of random block Schrödinger operators (RBSOs) in dimensions 1 and 2, which naturally extend the Anderson model by replacing the random potential with a random block potential. Specifically, we focus on two RBSOs -- the block Anderson and Wegner orbital models -- defined on the $d$-dimensional torus $(\mathbb Z/L\mathbb Z)^d$. They take the form $H=V + λΨ$, where $V$ is a block potential with i.i.d. $W^d\times W^d$ Gaussian diagonal blocks, $Ψ$ describes interactions between neighboring blocks, and $λ>0$ is a coupling parameter. We normalize the blocks of $Ψ$ so that each block has a Hilbert-Schmidt norm of the same order as the blocks of $V$. Assuming $W\ge L^δ$ for a small constant $δ>0$ and $λ\gg W^{-d/2}$, we establish the following results. In dimension $d=2$, we prove delocalization and quantum unique ergodicity for bulk eigenvectors. Combined with the localization result from arXiv:1608.02922, which holds under the condition $λ\ll W^{-d/2}$, this provides a rigorous proof of the Anderson localization-delocalization transition as $λ$ crosses the critical threshold $W^{-d/2}$. In dimension $d=1$, we show that the localization length of bulk eigenvectors is at least of order $(Wλ)^2$, which is believed to be the correct scaling.