Europe's largest 10km run had more than 35,000 runners last year and there will also be a half-marathon this time.
"Manchester is a truly resilient city and we look forward to successfully hosting these great sporting events," said city councillor Luthfur Rahman.
Earlier, Chelsea cancelled their Premier League victory parade, which was due to take place on Sunday.
The club say it would be "inappropriate" with the UK terror threat at its highest level after Monday's bombing killed 22 people and injured 64.
Thousands expected at Great Run
Greater Manchester Police and the city council had already said athletics' Great CityGames could take place in Manchester on Friday evening.
Now they have given the go-ahead for the Great Run, with additional security measures expected to be in force.
Rahman, the council's executive member for culture and leisure, said: "The Great CityGames and Great Manchester Run are two of the real highlights of Manchester's sporting calendar.
"We know that thousands of Mancunians have been looking forward to taking part, or cheering the athletes on, so I am pleased and proud to confirm that these fantastic events will be held as planned this weekend."
Olympic long jump champion Greg Rutherford is among those lined up to take part on Friday, with Sunday's field including Ethiopia's triple Olympic champions Kenenisa Bekele and Tirunesh Dibaba.