So the Olmert era has ended. The fight will now begin as to whom will take over Kadima, the party founded by former premier Ariel Sharon as the political "big bang" to establish a centrist Israeli party.
This is not going to be an ideological battle, as there is precious little ideological content to Kadima. It is going to be all about the power struggle between the two front-runners: Foreign Minister Tzipi Livni and Transport Minister Shaul Mofaz.
Livni is on the doveish side of Kadima, supports the negotiations with Syria and has developed a good relationship with Ahmed Qurei, her Palestinian negotiating counterpart.
She has made her presence felt on the international stage, where she is considered a serious player by foreign dignitaries who are rather delighted by her brief past as a Mossad agent.
Livni will make much of her "Ms Clean" image within the party, as well as the fact that polls indicate the Israeli public see her as the most electable candidate.
Mofaz, on the other hand, is a hawk who made headlines with dire warnings of an "inevitable" Israeli military strike on Iran some months ago. But his past as an IDF Chief-of-Staff and Defence Minister give him serious security credentials.
Although he only began his political career five years ago, he has the operating skills of an old-guard Likudnik, building up support from local power-brokers and lobbyists.
Theoretically, whoever wins the Kadima primaries will go on to form a new coalition when the Knesset returns in October. That is likely to be a remake of the present coalition with Labour, whose leader and current Defence Minister Ehud Barak is keen to avoid elections.
Although he did manage to gain some credibility by demanding Kadima replace Olmert, Barak is dangerously weak, having failed to boost his party's ratings throughout his tenure.
Opposition leader Binyamin Netanyahu would love to see elections as soon as possible, as all the polls indicate that, if they were held now, he would be the biggest winner.
And he could be the biggest loser if a smooth transition ensures a new and stable Kadima-led coalition, which would leave him sidelined and frustrated for another two years.
Even worse, if Livni becomes Prime Minister, Netanyahu will have to suffer the indignity of being leapfrogged by the woman to whom he gave her first public position as head of the state-owned companies authority, 12 years ago.
All he can do is either bolster Mofaz's candidacy - as a right-winger, he would likely bring the Likud back into the government - or try to derail a Livni administration by persuading Shas to bolt.
Moribund as it is, the peace process is also set to suffer from the current turmoil and political machinations.
Any meaningful negotiations with either Syria or the Palestinians are unlikely in this state of flux, and even after the new appointments are made there is no guarantee of an automatic resumption.
And then there is Iran's nuclear programme; a top priority across the Israeli political spectrum and the top issue for the next prime minister, whoever he or she will be.
But the key to progress will be the stability of any governing coalition. It is unlikely that we will have to wait for new elections until they are due in 2010.
Extracts from his farewell speech
Now is the time in which I must make a decision. I do not make it out of a feeling that I cannot fulfil my duties. I believe with all my heart in my ability to continue to serve, the same as I believe in my innocence... but the mudslinging crusade which is being conducted against me, even by decent people who are truly concerned for the state and its image, brings up a question that I cannot and will not avoid. What is more important? My personal justice, or the public good? My personal justice is very important to me...but in choosing between considerations relating to my status and my ability to fight for my truth, and the considerations of what is best for the country- it is the latter that decide.
As a citizen in a democracy I have always believed that when a person is elected Prime Minister in Israel, it is the duty even of those who opposed him in the ballot to want him to succeed. But instead of gaining this basic trust, I found myself subjected to a wave of investigations and criticism immediately upon assuming office.
Almost from day one, I had to repel vicious attacks as I was making critical decisions that are pertinent to the security of Israel and its existence. I am the prime minister and am naturally a target in political struggles.
But any intelligent person will understand that things have been blown completely out of proportion. Have I made mistakes throughout my long years of activity? Definitely yes and I regret them and am sorry for them. But is the true picture being presented to the public? Definitely not.
I want to make this clear: I am proud to be a citizen in a nation in which a prime minister can be investigated like any citizen. The prime minister is not above the law, but he is in no way below it.
