In a statement, Yorkshire said the elevation of White, who dropped out of England contention last season, was no slight on middle-order batsman McGrath's leadership skills.
"Following discussions with Anthony, it was decided that it was in his best interest, in pursuing his England international career, that he should concentrate on this aspect and relinquish the Yorkshire captaincy for the time being."
White, who played two matches for Australian state side Victoria after being schooled in Bendigo, made his Yorkshire debut 14 years ago and now faces the challenge of reviving the fortunes of English County cricket's most successful team.
Yorkshire won a record 30th championship title in 2001 but were relegated to the second division the following season.
In 2002 the Headingley-based team failed to gain promotion and were also demoted to the second division of the One-day National League.
White, one of whose recent predecessors as Yorkshire skipper is his brother-in-law, Australia batsman Darren Lehmann, has played 30 Tests and 51 One-day Internationals for England.
He suffered an unexplained blackout in 2000 but recovered to star in the home series against the West Indies where his sharp pace bowling off a short run but featuring a strong shoulder action proved effective.
However, the emergence of Andrew Flintoff and a side injury, which he aggravated on the 2002-03 tour of Australia, have curtailed his Test appearances.
Despite not being fully fit White was an ever-present in England's 2003 World Cup campaign but a rib problem sustained during the tournament restricted him to just nine championship matches last season and even prompted the all-rounder to consider retirement.
England paceman Darren Gough had been sounded out about becoming Yorkshire skipper by new director of cricket David Byas, who led the team to championship glory three years ago.
But earlier this month the Test-retired Gough quit the County saying he wanted to play for a club nearer to where his children are based in the south of England.
Darren Gough quits Yorkshire County