The champions have won back-to-back Premier League games for the first time this season since Shakespeare was put in temporary charge in the wake of Claudio Ranieri’s sacking.
And the 53-year-old, who has spent seven of the past eight years on the club’s coaching staff, has been given the task of steering City to survival between now and the summer.
Shakespeare’s first task as permanent boss will be to prepare the side for Tuesday’s Champions League game against Sevilla.
Leicester go into the second leg of the last-16 tie 2-1 behind.
EPL RESULTS
AFC Bournemouth
3 – 2
West Ham United
Everton
3 – 0
West Bromwich Albion
Hull City
2 – 1
Swansea City
Liverpool
2 – 1
Burnley
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