The 44-year-old will work alongside Andy Hessenthaler, who was appointed as Orient boss last week.
Former Southend, Birmingham and Peterborough defender Edwards joined the east London outfit in 2009 and has been coaching in the club's academy.
He assisted with first-team affairs at the end of last season while Hessenthaler was in caretaker charge.

He said his party was on course to win its first ever seats in Cardiff - where it is campaigning heavily - and in the Northern Ireland and London Assemblies.
It was "50-50" whether the party would gain representation in the Scottish Parliament for the first time, he said.
He declined to put a target on UKIP gains in English council elections.
UKIP is campaigning on multiple fronts as it seeks to become the only UK party to get people elected to the National Assembly of Wales, the Scottish Parliament and the Northern Ireland Assembly as well as the Greater London Assembly.
The party has focused much of its time and resources in Wales, where it won 13% of the vote in last year's general election.
Opinion polls suggest UKIP is set to win seats for the first time despite a row over its candidate selection process.
Mr Farage told the BBC's Daily Politics: "There will be a breakthrough in Wales. I think we are going to win five seats - we may do slightly better than that. Let's see."
As for England, Mr Farage would not be drawn on how many seats it would gain but said its record in local government was a good one and he predicted it would consolidate its position in its existing strongholds in Essex and South Yorkshire.
"We will make gains. To try and guess how many is virtually impossible. In Thurrock, I think we will become the biggest party on that council, in Rotherham we have a chance of becoming the biggest party on that council.
"There are 500 local UKIP councillors. Our local base is growing, the people who have had elected have behaved, on the whole, pretty well and been very diligent and worked very hard. Yes, we will improve."
There has been speculation about the future of the party, and a possible change in direction, whatever the outcome of June's referendum on EU membership.
Mr Farage said if there was a narrow vote to stay in the EU, a lot of Conservative and Labour supporters would be unable to reconcile themselves with the result and their party leadership's stance and UKIP could find itself "a lot bigger than it is now".
If there was a vote to leave, he said UKIP would need to "stay around" to ensure that the people's will was "implemented" but he conceded that it would need to show it could talk about issues other than Europe.
And he rejected suggestions that UKIP - which only managed to get one MP elected in last year's general election despite winning 12% of the vote - was treading water nationally, citing a recent YouGov opinion poll which put it on 20%.
"We are now at the highest we have ever been as a party - what more can I do?"

The best picture winner also garnered best director awards for Richard Linklater and best supporting actress for Patricia Arquette.
It was shot over more than a decade to capture the passage of time in one boy's life from age 5 to 18.
The annual critics awards are typically viewed as a pre-cursor to the high-profile and coveted Academy Awards.
Other winners include actor Timothy Spall - named best actor for British painter JMW Turner in Mr Turner - and best actress Marion Cotillard for her roles in The Immigrant and Two Days, One Night.
Actor JK Simmons won a best supporting actor prize for his role as a terrorising music teacher in Whiplash.
The Lego Movie won best animated film, while Ida was named best foreign film. Citizenfour, about US intelligence whistleblower Edward Snowden, won for best documentary film.
Presentation of the awards is scheduled for 5 January in New York.
The New York Film Critics Circle, founded in 1935, counts members representing magazines, newspapers and online publications.
The awards are considered a bellwether for the Oscars, which will air on 22 February.
League Two club Leyton Orient have appointed Andy Edwards as assistant manager.
[NEXT_CONCEPT]
UKIP will win at least five seats on the Welsh Assembly as part of a UK-wide "breakthrough" in Thursday's polls, its leader Nigel Farage has said.
[NEXT_CONCEPT]
Boyhood, a film 12 years in the making, has won top honours at the New York Film Critics awards.