Albion held talks with Rangnick last month as they continued their search to find Roy Hodgson's successor.
And the 53-year-old is believed to have agreed a deal to take the managerial reins at The Hawthorns, having first met with Albion officials when a guest for the final home Premier League game against Arsenal on May 13.
Compensation was not an issue as Rangnick has been without a club since leaving Schalke eight months ago because of exhaustion.
He nudged ahead of Birmingham boss Chris Hughton after it emerged Blues were looking for around £2million in compensation.
Rangnick had two spells at Schalke, leading them to the semi-finals of the Champions League in 2010-11, in addition to a four-year stint at Hoffenheim.
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Support the USA national team with an official 2013 Centennial soccer jersey from Nike. Its Official.
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