The event, which will take place in the city over the weekend, is expected to attract tens of thousands of people and will include the annual Pride parade on Saturday.
This year’s theme is inclusive education, in support of a campaign for a government commitment to tackle high rates of homophobia, biphobia and transphobia in Scottish schools.
In June, 49 people were killed and dozens more were injured in an attack on a gay night club in Orlando, Florida.
Ms Constance, who is due to speak at the Equality Network’s float, said the festival is both a celebration of LGBTI communities and a stand against hate crimes.
She said: “Pride Glasgow is an opportunity to celebrate LGBTI communities and to present a unified front by standing and marching together against hate crime.
“Showing this solidarity is even more important in the wake of recent atrocities in Orlando and the persecution LGBTI people in other parts of the world face on a daily basis.
“Scotland should be proud of the progress we’ve made to tackle LGBTI inequalities but we cannot be complacent. To eradicate hate crime we all need to take responsibility for challenging any prejudice and discrimination in our society.
“We will continue to work to address any inequalities that exist by uniting against hate crime and updating our gender recognition laws.”
Equality Network director Tim Hopkins said: “The event is themed around the vital importance of making our education system LGBTI-inclusive, to address prejudice and ensure that LGBTI young people know that their identity is fully respected and valued.
“We also very much welcome the Scottish Government’s commitment to bring our gender recognition law up to international best practice, and we look forward to helping the Government ensure that Scotland retains its place amongst Europe’s leaders on legal equality for LGBTI people.”