Club president Ken Vaughan confirmed on Wednesday that the Thame-based club had opted for the duel approach.
Evans is the club's director of rugby with many years experience at Kingsey Road, but has also coached the first team before.
Bowers, the RFU development officer in Bucks, coached Tring to promotion in the London leagues last season.
They take over from Brodley, who was axed last week.
A statement issued by the club blamed Chinnor's poor run of results this season, which has only seen them win twice in National Division Three South.
The statement said: "It is with considerable regret that Chinnor RFC confirm the departure of head coach John Brodley.
"John has made a significant contribution to the club over these past six years.
"His loyalty, dedication and work ethic are unquestioned.
"Unfortunately, results have not gone our way this season, culminating in another heavy loss this past Saturday.
"As always in these circumstances, morale and confidence takes a battering.
"It was becoming increasingly difficult for both players and coach to remain positive and focused.
"When this occurs alternative options have to be considered.
"This is not to cast any criticism in John's direction, but possibly a different approach needs to be adopted. With this in mind we have taken the most difficult of decisions to relieve John of his duties. We wish him well."