Political deadlock after the inconclusive 6 May election and the inability of warring parties to forge a coalition government have forced Greece to hold a second election as the threat of economic collapse grows (see background).
Bakoyannis's small liberal Democratic Alliance won 2.55% of the vote on 6 May, less than the 3% required to enter Parliament.
Bakoyannis is the daughter of veteran Greek politician Constantine Mitsotakis. In 2010, she had to leave New Democracy (ND), because she supported the EU/IMF backed austerity measures, which at that time ND rejected.
Bakoyannis gave the Democratic Alliance a liberal European affiliation, while ND is affiliated with the European People´s Party. In the European Parliament, the Democratic Alliance has only one MEP, Theodoros Skylakakis.
Bakoyannis was foreign minister from 2006 to 2009, the highest position ever held by a woman in a Greek cabinet. She was mayor of Athens from 2003 to 2006, the first female mayor of the Greek capital.
In the recent election, the pro-bailout ND came first with 18.9% and the leftist SYRIZA, riding a wave of discontent and promising to end the austerity policies that are deepening economic hardships, was second with 16.8%.
European leaders say that if the next Greek government spurns the bailout, they will have no choice but to cut off funding, which could force the country out of the eurozone.
The prospect sent the single currency tumbling last week and hurt the bonds of Spain and Italy, countries that could be next in the firing line if Greece collapses.
"I welcome the decision of Ms Bakoyannis to suspend the operation of her party and take part in our common effort," ND leader Antonis Samaras said.
"We have called for a big patriotic front to unite all citizens who will not let the country surrender to populism and be led to bankruptcy, international isolation and be forced to exit Europe," he said.
The latest opinion polls show that SYRIZA has edged ahead of ND, which has also regained some of its lost support.
The party that comes first in elections in Greece gets a 50-seat bonus in the 300-member Parliament.
"We will defend our country's future and its European perspective. Our goal is to get the country out of the crisis but keep it inside Europe and the euro," Samaras said.