Home Secretary Theresa May has said the murder of soldier Lee Rigby "united the entire nation in condemnation".
She was among a range of politicians, campaigners and faith groups to pay tribute to Fusilier Rigby and denounce the actions of Michael Adebolajo and Michael Adebowale.
Mrs May said: " The sickening and barbaric murder of Drummer Lee Rigby united the entire nation in condemnation and I welcome the jury's decision.
"But we must not forget that this appalling and public act of violence and terror also robbed his family and loved ones of a brave, young man with his life ahead of him. My thoughts are with them at this difficult time.
"Violence and extremism of any kind have absolutely no place in our society and cannot be justified. In the wake of Lee Rigby's murder, the Prime Minister set up the Extremism Task Force, which recently announced new measures to tackle extremism and radicalism across the UK.
"We have some of the toughest counter-terrorism laws in the democratic world and we are resolute in our determination to counter the threats to our way of life posed by extremist behaviour and ideologies."
Shadow home secretary Yvette Cooper said: " This was a vile and sickening attack on an unarmed and innocent man on the streets of London and our thoughts remain with the family, friends and colleagues of Lee Rigby on a day when his murderers have been found guilty.
"The police and security services have worked tirelessly to bring those responsible to justice.
"The message from this court case, from the community in Woolwich and from us all is that acts of barbaric cruelty will do nothing to diminish our resolve to stand up to extremism in all its forms.
"The local community, and people across the country, have refused to allow murderers and extremists to divide us."
Mayor of London Boris Johnson said: " The murder of Lee Rigby was barbaric, heinous and completely unjustifiable.
"Fusilier Rigby was a dedicated and professional young man whose life was taken in the most casual, brazen and horrific fashion, in broad daylight on the streets of London.
"This is a city that prides itself on tolerance, diversity and openness, values that stand in marked contrast to the actions of Lee's killers.
"Lee's courage, and that of those members of the public who sought to protect him, as well as the extraordinary bravery of the police officers involved are what we should remember today."
Sue Hemming, head of special crime and counter-terrorism at the Crown Prosecution Service, said: " The murder of Fusilier Rigby was brutal and its perpetrators carried out one of the most savage offences ever prosecuted by our counter-terrorism lawyers.
"As a soldier, this young father had dedicated his life to keeping people safe, including from the threat of terrorism. That dedication to his country cost him his life and was in stark contrast to the appalling conduct and extremist views of the men who murdered him."
Fiyaz Mughal, director of Faith Matters, an interfaith and anti-extremism organisation, said: " Both Michael Adebowale and Adebolaje talked about the killing of 'innocent civilians in Muslim lands' as some sort of justification for their sick actions.
"Speaking as a Muslim, leading an organisation which has had to fight a backlash against my fellow believers as a result of these men's murderous deed, I am shocked by their lack of empathy for their victim whilst claiming pain for those they have never met.
"There is a complete denial, a complete void of responsibility, on the cause and effect of their actions.
"Carrying out their murder in broad daylight in the capital means they must have known they would feed into those 'counter-jihad' networks and organisations who paint a 'clash of civilisations' picture of Muslims as being a one-dimensional block, hell-bent on taking over. Adebowale and Adebolaje played right into their hands."
Nick Lowles, chief executive of anti-racism campaign Hope Not Hate, called for further efforts to ensure radical preachers such as Anjem Choudary can face the "full force of the law".
He said: " Like all right-minded Britons, we were left sickened and appalled by the gruesome murder of Lee Rigby.
"We've campaigned for years against the malignancy of fascism and groups such as the British National Party (BNP) and English Defence League (EDL), yet we've seen how hate preachers such as Anjem Choudary feed the fires and vile myths perpetuated by these anti-Muslim haters.
"In fact, ordinary Muslims are his first victim, because of the demonisation of Muslims that results. EDL members went on a rampage in Woolwich the night of the killing, and there was a large spike of anti-Muslim incidents in the weeks and months following - a trend that is sadly still continuing."
He added: "Enough is enough: the Government must do more than pay lip service to the problem of hate preachers. It is time we took action against those who radicalise and motivate those who go on to commit acts of terror.
"Anjem Choudary should face the full force of the law, under new powers the Prime Minister tells us he is bringing in."
Farooq Murad, secretary general of the Muslim Council of Britain, said: "The murder of Drummer Lee Rigby was truly a barbaric act.
"Muslim communities then, as now, were united in their condemnation of this crime.
"This was a dishonourable act and no cause justifies cold-blooded murder."