"Trust in the values of our people and in our ability to rebuild the economy," Mr Temer said.
He has named a business-friendly cabinet that includes respected former central bank chief Henrique Meirelles as finance minster.
Ms Rousseff denounced her removal as a "farce" and "sabotage".
Mr Temer was the leftist Ms Rousseff's vice-president before withdrawing his party's support in March. She has accused him of involvement in a "coup".
After Wednesday's all-night session that lasted more than 20 hours, senators voted by 55 votes to 22 to suspend her and put her on trial for budgetary violations.
In her final speech on Thursday afternoon, she again denied the allegations and vowed to fight what she called an "injustice" by all legal means.
Mr Temer, 75, has now taken over as president for up to 180 days - the maximum time allowed for the impeachment trial of Ms Rousseff, 68.
He said: "It is urgent to restore peace and unite Brazil. We must form a government that will save the nation."
Stressing that "economic vitality" was his key task, he added: "It is essential to rebuild the credibility of the country at home and abroad to attract new investments and get the economy growing again."
But he also said Brazil was still a poor nation and that he would protect and expand social programmes.
"Let's stop talking about crisis. Let's work instead," he said.