I read this many years ago, possibly 30 years or so. Primary audience as I recall is the more mature sci-fi crowd.
The story is about a lone spaceship captain flying interplanetary cargo hauls in our solarsystem. The setting is one of a slightly decaying society, with the usual problems, trash, pollution etc. There are several planets with mining facilities and colonies, and our intrepid captain tenders to these, in a private business, carrying plutonium and similar stuff. On one of these hauls, he receives a mysterious transmission/message, that instructs him to find a woman and at a given time the two of them and their ship will be sent to Andromeda to start human civilization again, away from their current decay. He actually finds a woman and his ship is sent off to Andromeda, by the same entity that gave him the message in the first place.
The book was a paperback, pocket-sized, and had cover-art depicting the captain sitting in the cockpit of his ship, seen from the outside. The book also had a diagram of his ship inside the covers. The ship looked almost like the front cockpit area of the space shuttle, tacked on to a very wide and flat, rectangular cargo ship. I seem to recall that there was a numbered explanation to different parts of the ship diagram, but not sure. Name of the book is unknown, author is unknown. Any help is greatly appreciated!