Many different techniques can be used. ImageMagick has FX language that can perform complex calculations.
convert a.jpg b.jpg -fx 'Wi=w/2; Hi=h/2; hypot(Wi-i, Hi-j) < 50 ? u : v' c.jpg
For example...
convert -size 100x100 PLASMA: a.jpg
convert -size 100x100 GRADIENT:LIME-ORANGE b.jpg
convert a.jpg b.jpg -fx 'hypot(50-i, 50-j) < 50 ? u : v' c.jpg
Update with another technique.
A faster approach can be leveraging image mask(s) of the shape you wish to crop, and compose/composite it between both images. It'll require a format that supports alpha channels, but only for the initial work. For example...
Create a circle mask, and copy values to alpha channel.
convert -size 100x100 xc:White -fill Black \
-draw 'circle 50 50 50 5' -alpha Copy mask.png
convert \( a.png mask.png -alpha Set -compose Dst_Out -composite \) \
b.png -compose Dst_Atop -composite c.png