The news about Mr Regev's appointment came amid a flurry of senior diplomatic postings announced by Mr Netanyahu, the acting foreign minister.
Some of those appointments have drawn criticism.
Science Minister Danny Danon's appointment to the UN had been rumoured for weeks, but still prompted shock when it came.
The outspoken Mr Danon, one of the most right-wing of a pretty radical Likud list, was fired last year by the prime minister for publicly attacking his Gaza strategy as "leftish limpness".
How this advocate of annexing the West Bank will represent a prime minister who, at least publicly, has committed to the two-state solution is still unclear.
The official statement from the prime minister's office on his appointment was somewhat less than effusive and it is widely seen as an indication of Mr Netanyahu's low opinion of the UN (despite having launched his own career as a youthful ambassador there) and the fact that he was interested in shipping Mr Danon as far away from the cabinet table as possible.
Surprisingly perhaps, the appointment of Dani Dayan as the new ambassador to Brazil drew the most praise.
Mr Dayan is a former chairman of the Yesha Council and has been the settlers' most effective spokesman, in both Israeli and foreign media. Despite his politics, Mr Dayan is highly popular in Israeli political circles, for his courteous manner and intelligent debating skills. His choice was almost universally hailed by the right and left.
The choice of Fiamma Nirenstein for the embassy in Italy was surprising as she is barely known in Israel - unlike in Italy, where she was a prominent journalist and parliamentarian.
While Israel has often been represented by ambassadors returning to their countries of birth, none have been appointed after such a short time living in Israel. Ms Nirenstein made aliyah only two years ago and she is already heading back to the television studios in Rome she knows so well. This has caused grumbling within the local Jewish community that it will give grounds for some to accuse Italian Jews of "dual loyalties".
There are still a few more senior diplomatic appointments to be made. One of the trickiest is the ambassador to Russia. The job was supposed to go to Naomi Ben Ami, a seasoned diplomat, born in the former Soviet Union, whose CV includes being Israel's chargé in Riga, political attaché in Moscow, ambassador to Ukraine and, for the last nine years, heading Nativ, the government agency in charge of maintaining contact with Jews living throughout the former Soviet Union.
Ms Ben Ami has only drawback: she is seen as a protégé of former foreign minister Avigdor Lieberman, who promised her the job. That was seen as a black mark and she is being forced to wait to see if her appointment will go ahead.
A major appointment by the former foreign minister that has been approved is that of former ambassador to Britain, Zvi Hefetz, as Israel's next man in Beijing.
Mr Hefetz is a rare creature, both a successful businessman who has built a second career as a diplomat (he is currently ambassador to Austria) and also trusted by all main political players.
He was sent to London by late prime minister Ariel Sharon, to Vienna by Mr Lieberman and Mr Netanyahu has promoted him to one of the top envoy roles. He has a rare set of political skills that will serve him well in China.
