But the Labour leader snubbed leading moderates in the party like Yvette Cooper and Chuka Umunna who had been tipped to make a comeback to the frontbench.
He retains the co-national campaign coordinator role alongside Mr Lavery.
And Mr Corbyn handed the gig to Ms Laird, who snatched back Gordon Brown's former constituency of Kirkcaldy and Cowdenbeath.
The former leadership contender is reportedly going to join Labour's top team when Mr Corbyn announces his reshuffled shadow cabinet later this week.
"My priorities are the things that people told me are important to them in the General Election campaign: that's jobs, housing and public services".
One senior shadow cabinet figure said the election result had vindicated Mr Corbyn's strategy but that Labour needed to do more to be seen as a government in waiting.
The Edinburgh South MP was replaced by an MP from the northeast of England, David Anderson, who also served as Northern Ireland secretary before standing down at the election.
And Andrew Gwynne was made Shadow Secretary of State for Communities and Local Government and Co-National Campaign Coordinator.
But a spokesman for Mr Corbyn said the five appointments are the only changes being made to the shadow cabinet.
Brent MP Dawn Butler, a longtime Corbyn loyalist who resigned over the party's stance on article 50, will return as shadow minister for diverse communities.
Mr Corbyn said on Tuesday that his party should be in "permanent campaign mode" in light of Theresa May's attempts to form a minority government with the backing of the Democratic Unionists.