Gibb recieves a knighthood for "political and public service", while Slack's CBE is for "public service".
In addition, Kirsty Buchanan, the current comms director at Ministry of Housing, Communities and Local Government and a former special adviser to May as PM, becomes an OBE for her "political and public service".
Gibb, former editor of the BBC's Daily & Sunday Politics show and executive editor of the broadcaster's Andrew Marr Show and This Week, was hired as comms director in summer 2017.
He replaced Katie Perrior, who resigned following May's calling of the general election that year.
Former Daily Mail political editor Slack worked under May's administation from early 2017.
The Resignation Honours has come in for criticism this morning, particularly around the appearance of former key May advisers Fiona Hill and Nick Timothy, who both became CBEs. Hill and Timothy were widely seen as the architects of the Conservative's poor showing in the 2017 general election.
Sir Robbie Gibb. Sir Gavin Barwell. Fiona Hill and Nick Timothy CBE. For what? The honours system passed its sell-by date decades ago. This one could be a tipping point for reform— Alastair PEOPLE’S VOTE Campbell (@campbellclaret) September 10, 2019
There has also been criticism of the appearance of Geoffrey Boycott. The former England cricket captain, who has received a knighthood, was convincted of assaulting his partner in 1998.
Sir Geoff Boycott ‘doesn’t give a toss’ what Women’s Aid says about his knighthood while having an assault conviction. In 1998 a French court heard he punched then girlfriend Margaret Moore 20 times, which he denied. He was given a 3 mth suspended sentence. Do YOU ‘give a toss?’ pic.twitter.com/kq1pquHc8w— Victoria Derbyshire (@vicderbyshire) September 10, 2019