Former Aberdeen and Manchester United manager Sir Alex and the Aberdeen-born singer featured in almost 2,000 public responses.
Their achievements will be celebrated at Provost Skene's House.
The building will reopen following the completion of the Marischal Square development this summer.
The Hall of Heroes:
The 10 were picked from 50 candidates during a three-week vote.
Aberdeen City Council leader Jenny Laing said: "The public's contribution has been tremendously valuable and will help ensure the attraction has widespread appeal.
"The stories and achievements of our heroes - indeed all the candidates - clearly resonated with residents."
Percussionist Dame Evelyn Glennie said: "I am hugely honoured to have been selected."

Voters will go to the polls again after Prime Minister Ahmet Davutoglu abandoned efforts to form a coalition government.
Mr Davutoglu's AK Party lost its 12-year majority rule in Turkey in elections in June largely because of the success of the pro-Kurdish HDP.
Coalition talks with the nationalist MHP and main opposition CHP failed.
The political uncertainty comes amid rising violence in Turkey and neighbouring Iraq and Syria.
President Erdogan will ask Prime Minister Davutoglu early next week to form a temporary power-sharing government, senior officials said.
The Republican People's Party (CHP), which came second in June's vote, had asked for a mandate to try to form a new government.
But the president instead opted for a "re-run" of the elections.
Mr Erdogan, who founded the AK Party in 2001, previously denied allegations that he had undermined the coalition talks in order to force a new vote.
June's result appeared to block his plans to boost the powers of the presidency in Turkey.
The AKP secured 41% at the polls the last time around and had to seek support from a rival party to form a coalition government. But it failed to find agreement with both the CHP and Nationalist Movement Party (MHP).
An uneasy two-year ceasefire with the PKK fell apart last month, after a suicide bomb blamed on IS killed 32 young activists in the largely Kurdish city of Suruc, close to the Syrian border.
In recent weeks Turkish forces have carried out attacks on militants from the Islamic State (IS) group in Syria and have bombed Kurdish PKK camps mainly in northern Iraq.
Sir Alex Ferguson and Annie Lennox are among the famous names chosen in a poll to feature in a new Hall of Heroes tourist attraction in Aberdeen.
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President Recep Tayyip Erdogan has announced that Turkey will hold snap elections, expected on 1 November.