He even sent a text message from 29,035 feet/8,848 meters on the world's highest peak.
''To reach the summit and achieve world records with Motorola Z8 mobile handset is a once-in-a-lifetime opportunity,'' said Mr Baber from Everest Base Camp.
Baber first called a special voice-mail account and then made a second call to his wife and family.
''I've already climbed to the highest point in every country in Europe, so it was a natural progression to want to climb to the highest point in all the other continents,'' Mr Baber said.
''I want to be the first person to climb to the highest point in every country in the world. Fifty years ago, when Everest was first conquered, mountaineers couldn't even contemplate the kind of multiple challenges that we are setting ourselves today,'' he added.
The adventurer, who spent seven days climbing to the summit of Everest, had reached there in clear but windy weather.
Although bulky satellite phones have been used on Everest for some time, this is the first time anyone has made a mobile phone call from the top of the mountain.
The record only became available last year when China installed an antenna 12 miles from the peak, allowing line-of-sight transmission with the summit. Special batteries for Mr Baber's handset were taped to his body to ensure they stayed at a high enough temperature to power the phone.
Mountaineers typically only stay on Everest's summit for 15 minutes because of the extreme conditions.
Mr Baber and his team will now make a gradual descent down the mountain side.
The new records are the latest in a long line for Mr Baber who, at 29, became the fastest man to scale the highest peaks of every European country in 835 days. He also holds the world record for climbing more of the world's highest points than any other person.