Sheikh Mohammed bin Zayed al-Nahyan was met on his arrival by Emir Sheikh Tamim bin Hamad al-Thani, the emir's office said. Qatar is currently hosting soccer's World Cup,
The visit "is another step towards strengthening Persian Gulf solidarity and joint action," Anwar Gargash, diplomatic adviser to the UAE president, said on Twitter.
Saudi Arabia, the UAE, Bahrain and Egypt early last year ended a 3-1/2 year embargo of Qatar, but ties between Doha and Abu Dhabi have not warmed at the same pace as those with Riyadh and Cairo, which re-established diplomatic ties with Doha.
Saudi Arabia's crown prince and Egypt's president attended the opening World Cup ceremony in Doha on Nov. 20 while the UAE sent Dubai's ruler, who is also the Gulf state's vice-president.
The political dispute that had seen Riyadh and its allies sever all ties with Qatar - over its support for Muslim Brotherhood they deem a threat to Persian Gulf dynastic rule and its ties with rivals Iran and Turkey - had shattered the six-nation Persian Gulf bloc.
UAE National Security Adviser Sheikh Tahnoon bin Zayed al-Nahyan visited Doha twice as part of Abu Dhabi's push to manage regional differences.
Bahrain and Qatar have yet to hold bilateral talks. Abu Dhabi, like Manama, has not appointed an envoy to Doha, but restored travel and trade links between the UAE and Qatar.
This allowed the UAE to benefit from an influx of fans attending the World Cup under partnerships by Doha for daily shuttle flights with neighboring cities such as tourism hub Dubai.