Industrial conglomerate United Technologies Corp. reached a deal to buy airplane-parts maker Rockwell Collins Inc. for $23 billion, in the biggest aerospace deal in history.

Both companies’ boards have approved a deal in which United Technologies will pay $140 a share in cash and stock, the companies said late Monday. Rockwell investors will get $93.33 a share in cash and the remaining $46.67 in United Technologies stock.

The...