Mr Alarcon, 49, a lawyer, replaced Rosalia Arteaga, 40. She was appointed interim president on Sunday in a compromise deal brokered by the military to end street protests.
There had been reports that once she was in the job Mrs Arteaga would not give it up. But she resigned on Tuesday night shortly before Congress voted in Mr Alarcon. She did, however, criticise Mr Alarcon's appointment and called for a referendum to change the constitution so that Congress could not dump a president and name its Speaker for the job.
Mr Bucaram, meanwhile, still claimed to be the country's legal president and called Mr Alarcon "a Judas, a traitor", for using a little-known law to get rid of him.
Mr Bucaram once relished the nickname "el loco," the madman, but no-one seriously considered him insane. Eccentric, certainly. He is now on a tour of South American capitals to push his line that he was illegally ousted and that the same thing could happen to other leaders in the continent.
Mr Alarcon is to call new elections next year, so that a new president can be sworn in in August 1998. He is expected to run, as is Mrs Arteaga. Mr Bucaram has said he will also run, although some Ecuadorean analysts doubt he will return from his current tour, as he may face corruption charges.
The recent turmoil began after Mr Bucaram, who ran for President as a populist last year and won easily, performed a policy about-turn and imposed a series of austerity measures. These included prices rises of up to 300 per cent on basic utilities, such as electricity and gas. He was also widely criticised for corruption, and for giving government jobs to his relatives and friends.
"The entire country is breathing easier because we have put this crisis behind us," said the armed forces chief, General Paco Moncayo.
Gen Moncayo, a key figure in the negotiations to end the crisis, was widely applauded when he appeared in Congress for the swearing-in ceremony.
The dispute over power generated widespread fears in Ecuador that if no one took charge, the military would seize control of the country themselves.