The Australian-born 25-year-old, who switched his allegiance to Britain in 2013, is joined in the main draw by Aussie Matthew Edben.
The news comes after Klein enjoyed some impressive results at Challenger tour events on the grass of Manchester – the city of his mother’s birth – and Surbiton.
Klein joins compatriots Kyle Edmund, James Ward and Liam Broady as wildcard recipients. With Andy Murray and Aljaz Bedene having made the main draw as of right, it takes the number of Britons in the men’s singles to six.
One more wild card for the men’s draw remains to be handed out, while there are four still available for the women’s singles, with one expected to go to Laura Robson provided she comes through her comeback from injury in Eastbourne unscathed this weekend.