The BBC's HD satellite stream will start broadcasting on 11 May with a promotional preview accessible to users of Sky's electronic programme guide.
Bleak House and part one of Planet Earth will be screened on the Sky service between 27 and 29 May.
"These are small but exciting first steps in the BBC's ambition to offer the option of high definition to all in the future," said the corporation's director of television Jana Bennett.
The new format would offer "a new standard of quality for licence fee payers", she said.
"We really feel that high definition will be the standard definition of the future."
Trial
The programmes will kick off a 12-month trial to test the technology and the audience's appetite for the format.
A separate deal between Telewest and the corporation's commercial arm BBC Worldwide means other BBC shows have been available in HD on cable since March.
But Telewest is also expected to join Sky in carrying the trial broadcasts in time for the World Cup.
Sky will launch its own HDTV broadcasts on 22 May, offering Star Wars movie Revenge of the Sith and US drama 24 in the initial line-up.
