Auteur: Nikolaj Nielsen
Rompuy is set to teach an EU "leadership and decision-making" course at the College of Europe in Bruges, Belgium starting next year.
The changing of the guard is the last element of the new EU team.
The European Parliament held elections in May, while the new European Commission began work on 1 November.
The arrival of Tusk is also a watershed moment for the EU - the Pole is the first ever VIP from a former Communist or Soviet state to take an EU top job since the 2004 wave of enlargement.
Meanwhile, EU lawmakers will on Tuesday start talks to get an agreement on the 2015 budget.
Negotiators from the three main EU institutions will discuss the European Commissionís new 2015 budget proposal.
Member states want to limit spending at Ä140 billion, while MEPs are demanding Ä146.4 billion, with the commission in between.
Itís also a busy week for MEPs as parliamentary committees hold numerous debates, policy discussions, and public hearings.
Some of the more noteworthy occur on Tuesday and Wednesday when special visitors and EU commissioners attend the various committees linked to their portfolios.
Fallen Russian oil tycoon Mikhail Khodorkovsky will be discussing human rights with MEPs in the foreign affairs committee.
MEPs in the parliamentís economic affairs committee will be debating the ďannual growth survey for 2015Ē, which sets out the commissionís broad outline on creating new jobs and ratcheting up economies.
The EU commissioner for trade Cecilia Malmstrom†i will also be at attending a session at the civil liberties committee on Wednesday.
But the commission has requested a closed-door presentation when its officials brief MEPs on an EU-US agreement which lays out rules on handing over EU citizensí data among other issues.
Transparency International, on the same day, is also set to release its flagship global corruption report.
Meanwhile, EU ministers for justice and home affairs will be meeting at the end of the week.
Justice ministers will be discussing data and the reformed EU bill on the issue on Thursday. On Friday, home affairs ministers are discussing the foreign fighters and a report by the European commission on the border-free Schengen zone.
With the EU celebrating the fifth anniversary of the charter of fundamental rights on Monday, the EU court in Luxembourg will the next day rule on a case with big implications.
It will say whether gay people can claim asylum in the EU on grounds they are persecuted over their sexuality in their home countries.