The charges are part of the Met’s Operation Elveden, a probe into illegal payments to public officials.
News International, which owns the Sun, told staff it would support Mr Webster.
The 53-year-old will appear at Westminster Magistrates’ Court on 26 March.
The official in the first charge cannot be identified for legal reasons, and the second – who has not been named – is understood to have been either a member of the armed forces or a Ministry of Defence employee.
Alison Levitt QC, principal legal advisor to the director of public prosecutions, said in a statement that Mr Webster was being charged with “two offences of conspiring to commit misconduct in public office, contrary to section 1(1) of the Criminal Law Act 1977”.
She added: “The first offence relates to allegations that Mr Webster, between July 2010 and August 2011, authorised payments totalling £6,500 for information supplied by a public official to one of his journalists.
“The second offence relates to an allegation that in November 2010, Mr Webster authorised a payment of £1,500 for information provided by an unknown public official.”
Staff at the Sun have been sent an internal memo by Mike Darcey, chief executive of News International, in which he describes Mr Webster as a “long standing and valued colleague” and that his “thoughts are with… his family at this time”.
Mr Darcey also told staff that News International would support Mr Webster through the legal process.
About 60 people have been arrested as part of the Metropolitan Police’s Elveden inquiry, which is being run alongside two other police investigations.
Operation Meeting is an inquiry into alleged phone hacking, while Operation Tuleta is an investigation into computer hacking and other privacy breaches.
Reprinted from BBC.