The pair, who were both elected unanimously, have served at City Hall since the inaugural Assembly elections in 2000.
As Chair Mr Johnson will preside over meetings of the full Assembly and represent Assembly Members and Londoners at public events.
Mr Johnson said he would “seek to Chair Assembly meetings in a way that allows rigorous cross examination of the Mayor, allows the Mayor the opportunity to answer questions succinctly, and enhances transparency and accountability.”
He added: “Above all, while I am happy to facilitate rigorous democratic debate, I will also remember that the real strength of the Assembly is when we speak truth to power, united with one voice on behalf of Londoners.”
The election of Mr Evans follows complaints from the Assembly’s Conservative group that they were being unfairly excluded from the Assembly’s top jobs by the other parties.
Since 2000 the roles of Chair and Deputy Chair have largely been held by parties who do not hold the Mayoralty.
During Ken Livingstone’s 2004-08 term as Mayor the posts were shared by the Liberal Democrat and Conservative groups. Since the election of Mayor Boris Johnson in 2008, they have been held by Labour, Green and Liberal Democrat AMs.
The three groups have also shared the chairmanships of Assembly committees which hold the Mayor and his agencies to account, voting in a block to ensure Conservative AMs aren’t elected to the posts.
The Conservative group, the majority of whom where not on the Assembly during the 2004-08 term, say such deals are unfair as all AMs are elected to hold the Mayor to account on behalf of Londoners.
Private talks were held between all four Assembly parties in recent days to find a way of addressing Conservative complaints.
The parties eventually agreed to the election of Mr Evans as Assembly Deputy Chair and fellow Tory AM Gareth Bacon as Chair of the Regeneration Committee.
Speaking after the meeting, Mr Evans said: “There are strong and deeply held political differences among Assembly Members but I know from my 13 years at City Hall that we all share the same aim, making London the greatest city on earth.”