Olympic gymnast Aly ­Raisman of Needham returned to the United States Monday with a big greeting on her ­Twitter account and a full week ahead of her.

“HELLO, AMERICA,” the gold medal winner told her 429,000 Twitter followers from New York on Monday morning, as she shared pictures of her checked bags via Instagram and Twitter. By midday, the outlines of a busy schedule of media appearances for Raisman and her four teammates on the US gymnastics team began to take shape.

Now dubbed the “Fierce Five,” the team of Raisman, McKayla Maroney, Jordyn Wieber, Gabrielle Douglas, and Kayla Ross is scheduled to appear on “Good Morning America” on Tuesday , and on the “Late Show with ­David Letterman” Tuesday night.

The five will also be on “The Colbert Report” on Wednesday night, according to Comedy Central representatives.

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Raisman was expected to stay in New York for a few days to do the rounds of talk shows, as she and her teammates experience a measure of freedom from their rigorous training and performance schedules with the end of the 2012 Olympics Sunday.

‘She is your mirror. . . . You are the best in the world for a moment.’

“She’s free right now to do whatever,” said Raisman’s coach, Mihai Brestyan, who ­arrived back in Massachusetts Monday.

Raisman will probably ­return home to Needham this week, her friends say. The town plans to host a parade and a rally for her, according to ­Sandy Cincotta, a town support services manager, probably later this week.

“I believe everyone who could possibly be there will ­attend,” Cincotta said.

After resting in Needham, Raisman is expected to embark on a 40-city countrywide tour with her US teammates later this month.

Raisman, who belongs to Newton’s Temple Beth Avodah, will also visit Israel for the first time, as she reportedly accepted an invitation last week from Diaspora Affairs Minister Yuli Edelstein, according to The ­Jerusalem Post.

Raisman, who paid tribute to her Jewish heritage by performing her gold medal-
winning floor exercise routine to “Hava Nagila,” accepted the invitation to visit Israel in a phone conversation with ­Edelstein on Friday, The ­Jerusalem Post reported.

Brestyan, who also coached 2008 silver medalist Alicia ­Sacramone , said he shared the honor and excitement of ­Raisman’s two gold medals and the bronze medal in London’s games.

“When you hear the US ­anthem for your work, and you see your student at the top of the world  . . . ” he said, pausing to let it sink in. “She is your mirror — you feel the same. You are the best in the world for a moment in your profession.

“Those moments are the best in the world; they feel fantastic. Nothing can replace that feeling.”

The gymnasts are scheduled to appear around 8 a.m. Tuesday on ABC’s “Good Morning America,” which runs 7 a.m. through 9 a.m., and on the “Late Show” at 11:35 p.m. on CBS.

Wednesday’s Colbert show will run on Comedy Central at 11:30 p.m., and clips from the episode will be on the show’s website Thursday.