"Mr Bush ran with the themes that he laid out in his inauguration. He is a man who thinks big and takes big risks," the BBC said in an analysis piece.
"And as his second term begins, he knows that he had only a short time to spent the political capital he thinks he earned in his re-election."
In his traditional annual speech before Congress, Bush outlined plans to spread democracy across the Middle East, took aim at Iran and Syria and urged US lawmakers to overhaul the state-run Social Security pension program.
Christoph Bertram, of Germany's influential SWP think-tank, said that Bush appeared to have learned after his first mandate that co-operating with allies "is worth the bother" and that he would do so "when it suits him."
The French newspaper Le Monde, one of the few in Europe to go to press after the speech, remarked that Bush was "sure of himself and more relaxed since his re-election", adding that his speech was "unusually detail-rich".
Like the BBC, it referred back to Bush's first press conference after his re-election in which he pledged to spend the "political capital" he claimed to have earned during the campaign to fight terrorism and revamp Social Security.
But Le Monde warned his "impressive package of reforms" could "quickly run up against cold, hard legislative reality" - midterm Congressional elections in 2006.
Germany's respected Der Spiegel magazine was struck by the spectacle of Bush's address, but it grudgingly praised the president's performance.
"Bush's State of the Union speech was a melodramatic show, full of tears and sharp attacks on the devils of this world," Der Spiegel said in its online edition.
"It demonstrated how the US president has developed from a mangler of the language into a smart speaker."
The German weekly put the improvement down to speech writer Mike Gerson, who was writing what was expected to be his last such address.
In terms of content, Spiegel noted in particular explicit threats against Iran and Syria, points also highlighted in the left-leaning French daily Liberation.
"Bush said he would work with the Europeans to get Iran to give up the bomb... but he also directly invited the Iranians to rise up against their government," Liberation noted in its online edition.
Spain's El Periodico focused on the Middle East, saying Bush's recommitment to the Israeli-Palestinian peace process would not resolve ongoing violence, and that elections would not end bloodshed in Iraq.
"Bush sees himself on the way to pacifying the wider Middle East after the high turnout in the Iraqi election and amid the new process of entente between the Israelis and the Palestinians.
"But the (Iraqi) elections, added to the extreme marginalization of the Sunni minority, could lead to a civil war," the Spanish daily warned in an editorial.
"And the rapprochement between (Israeli Prime Minister Ariel) Sharon and (Palestinian leader) Abu Mazen remains hostage to Hamas and Islamic Jihad."