The move was mooted last month after Keane spoke to Celtic about the opportunity to succeed Neil Lennon as manager, but ultimately decided not to take matters any further.
Lambert's coaching staff was significantly depleted last season when assistant Ian Culverhouse and football operations manager Gary Karsa were suspended and then sacked for unspecified disciplinary reasons.
Keane's appointment comes with the players due to return for pre-season training on Monday.
The former Sunderland and Ipswich manager returned to the game in November last year when O'Neill offered him the opportunity to return to the international fold.
- Sports & Recreation
- Paul Lambert
- Neil Lennon
- Ian Culverhouse