The former Deputy Chief Constable was confirmed in the top job at a meeting of Strathclyde Police Authority in Glasgow on Monday.
The post vacated by Mr Corrigan will now be filled by former Assistant Chief Constable Rhuaraidh Nicolson.
In turn, his position will be filled by Chief Superintendent Russell Dunn.
Mr House was appointed last week to head up Scotland's new single police force, which comes into being in April next year.
He has already said that as many as 3,000 support staff could be lost as he seeks to merge eight forces into one.

Cummings grabbed the only goal from the penalty spot in the 32nd minute after Grant Holt had been pulled down in the box by Gregor Buchanan.
Goalkeeper Alan Martin produced a smart save to prevent Andrew Shinnie doubling the lead.
Holt and Cummings also threatened as the Sons did little at the other end.
A third clean sheet made it five wins from five for leaders Hibs.
Match ends, Dumbarton 0, Hibernian 1.
Second Half ends, Dumbarton 0, Hibernian 1.
Daniel Harvie (Dumbarton) wins a free kick on the right wing.
Foul by Grant Holt (Hibernian).
Grant Holt (Hibernian) wins a free kick in the defensive half.
Foul by Craig Pettigrew (Dumbarton).
Attempt missed. Darren Barr (Dumbarton) header from the centre of the box misses to the right.
Robert Thomson (Dumbarton) wins a free kick in the attacking half.
Foul by Darren McGregor (Hibernian).
Attempt missed. Dylan McGeouch (Hibernian) right footed shot from long range on the left is close, but misses to the right following a corner.
Corner,  Hibernian. Conceded by Craig Pettigrew.
Substitution, Hibernian. Jordan Forster replaces Andrew Shinnie.
Foul by Paul Hanlon (Hibernian).
Robert Thomson (Dumbarton) wins a free kick in the attacking half.
Substitution, Dumbarton. Donald McCallum replaces Grant Gallagher.
Substitution, Dumbarton. Mark Docherty replaces David Smith.
Foul by Darren McGregor (Hibernian).
Robert Thomson (Dumbarton) wins a free kick in the defensive half.
Attempt missed. Robert Thomson (Dumbarton) left footed shot from the right side of the box is close, but misses to the right.
Hand ball by Josh Todd (Dumbarton).
Corner,  Dumbarton. Conceded by Darren McGregor.
Foul by Brian Graham (Hibernian).
Gregor Buchanan (Dumbarton) wins a free kick in the attacking half.
Attempt missed. Andrew Shinnie (Hibernian) left footed shot from outside the box is close, but misses the top left corner.
Attempt saved. Brian Graham (Hibernian) right footed shot from outside the box is saved in the centre of the goal.
Substitution, Dumbarton. Garry Fleming replaces Ryan Stevenson.
Attempt blocked. Paul Hanlon (Hibernian) right footed shot from outside the box is blocked.
John McGinn (Hibernian) wins a free kick in the defensive half.
Foul by Joseph Thomson (Dumbarton).
Corner,  Hibernian. Conceded by Joseph Thomson.
Corner,  Hibernian. Conceded by Josh Todd.
Attempt saved. Brian Graham (Hibernian) right footed shot from outside the box is saved in the top centre of the goal.
Foul by Grant Holt (Hibernian).
Josh Todd (Dumbarton) wins a free kick on the left wing.
Andrew Shinnie (Hibernian) is shown the yellow card for a bad foul.
Craig Pettigrew (Dumbarton) wins a free kick on the left wing.
Foul by Andrew Shinnie (Hibernian).
Attempt missed. Andrew Shinnie (Hibernian) right footed shot from outside the box is just a bit too high.
Substitution, Hibernian. Brian Graham replaces Jason Cummings.
Substitution, Hibernian. Dylan McGeouch replaces Marvin Bartley.
Campbell Corrigan has been named acting Chief Constable of Strathclyde Police following Stephen House's appointment to head Scotland's new single force.
[NEXT_CONCEPT]
Hibernian extended their perfect start in the Scottish Championship as a Jason Cummings goal proved enough to beat Dumbarton.