The midfielder had made no secret of his desire to return to Gresty Road, where he won the Johnstone's Paint Trophy during his time on loan last season.
The 21-year-old rejected a new deal with the Magpies, but the club rebuffed Crewe's initial approaches this summer with Steve Davis' side fearing a tribunal could be needed to dictate Inman's fee.
However, that has been avoided with the two clubs agreeing an undisclosed fee and Inman signing terms on a three-year deal with the Alex, for whom he featured 26 times last term.
Crewe are now waiting on the official financial agreement from Newcastle and hope their drawn-out pursuit will reach a conclusion so Inman can feature at Leyton Orient on Saturday.
"It is really close now and we are confident that it will finalised over the next couple of days," Davis told the club's official website.
"It isn't completely done and dusted because we are waiting for the finance agreement from Newcastle.
"Newcastle have been good about things. We have both been up front and honest about things and the relationship has been good. They rejected a number of our bids, which they are fully entitled to do. We got there in the end.
"I think we have got him for the right fee and there is a sell-on for Newcastle as well, which is only right because if he becomes the player we think he will and goes on then they have helped with his development as well. "