The president of parliament's centre-right EPP group Manfred Weber praised the appointment of Tusk as the new European council president, calling the decision, "an excellent one".
"With [Saturday's] decision on EU top posts, the EU is finally ready to work on the political decisions that are urgently needed," said the German MEP, adding that the decision by teh EU's heads of state and government to elect Tusk was "good for the EU".
"With [Saturday's] decision on EU top posts, the EU is finally ready to work on the political decisions that are urgently needed" - Manfred Weber
Weber also pointed to the move as a "strong symbol of the completion of the EU's eastern enlargement", with Tusk marking the first time such a prestigious post has gone to a member state from central and south-eastern Europe.
"Tusk is also a real European and a strong and experienced politician willing to work towards compromise in the European spirit," he concluded.
Co-presidents of parliament's Greens/EFA grouping Rebecca Harms and Philippe Lamberts also highlighted the further integration for eastern members marked by Tusk's appointment, calling the move "long overdue".
"[The Greens/EFA are] prepared for major clashes as Donald Tusk is known to be a convinced climate change sceptic and has also made questionable decisions on pensions and education policy in his own country" - Rebecca Harms and Philippe Lamberts
The two MEPs, however, sounded a note of caution, warning that they were "prepared for major clashes as Donald Tusk is known to be a convinced climate change sceptic and has also made questionable decisions on pensions and education policy in his own country".
Harms and Lamberts also raised concerns over Mogherini's clinching of the post of EU foreign affairs chief, saying that member states had again settled on "a candidate with little experience of foreign affairs" - accusations that dogged the incumbent foreign affairs chief Catherine Ashton throughout her time in office.
The Greens/EFA co-leaders expressed doubts over Mogherini's ability to "unify 28 foreign ministers on a common EU position", adding that the council of ministers for foreign affairs would continue to view the external action service and high representative as "unnecessary competition".
Weber, echoed the Greens concerns, calling on Mogherini to "compensate her scarce experience on foreign policies through dedication as quickly as possible". He also made clear the EPP group's intentions to "check her competence and challenge her" at the upcoming parliamentary hearings.
All candidates for the post of European commissioner are invited to public hearings by the appropriate parliamentary committees. They answer questions from MEPs to assess their ability to deal with the issues in their portfolios.
The committees' evaluations are then examined by parliament's president and political group leaders, with Weber urging that Mogherini "be given the chance to prove herself".
The Greens concerns, however, also centred around the lack of female representation among the commissioners-designate, saying that the Italian's appointment "does not resolve the issue of the demand for equal participation of women in the commission".
"It is not enough if out of a total of six top EU jobs, only one goes to a woman. The Greens/EFA group will only support the next commission if there are at least as many women commissioners as in the current one," they added.
"As liberals, we cannot support a commission with too few women..." - Guy Verhofstadt
Their comments chimed with pre-summit warnings from parliament's ALDE group president Guy Verhofstadt, who said, "As liberals, we cannot support a commission with too few women and one that does not properly reflect the pro-European forces within the parliamentary majority of conservatives, socialists and liberals.
"Let there be little doubt that such a skewed commission will not find a majority in the European parliament and will simply be rejected.
"It is crucially important that the new commission can start at once with tackling the ongoing crisis in the EU, but for this to happen, the European council must live up to its responsibility and ensure that the new commission is balanced both genderwise and politically, and that the pro-European liberal family is represented at the top of the European Institutions.
"If not, it will be impossible for us to support it," he concluded.