Candles will be lit by relatives of the victims during the private ceremony, before an olive tree - known as the Tree of Healing - is planted in the cathedral grounds using compost from floral tributes left on the bridge in the aftermath of the murders last year.
A procession from the cathedral to Southwark Needle, at the corner of London Bridge and Duke Street Hill, will take place following the ceremony, and a minute's silence will be held at 4.30pm.
The Dean of Southwark, The Very Revd Andrew Nunn, who will host the service of commemoration, said the Tree of Healing will be "a constant reminder to us all of those who were harmed but also of the importance of our communities coming together to stand against violence in all its forms".
A digital book of hope will be available at Southwark Cathedral throughout the weekend for the public to sign.
Ahead of the day's commemorative events, the Prime Minister recalled the "stories of courage" which emerged from the attack.
She described it as a "cowardly attempt to strike at the heart of our freedoms by deliberately targeting people enjoying their Saturday night with friends and family".
Mrs May said: "Today we remember those who died and the many more who were injured, and also pay tribute to the bravery of our emergency services and those who intervened or came to the aid of others.
"The many stories of courage demonstrated that night will always stay with me - such as Ignacio Echeverria, who died after confronting the terrorists with the only thing he had, his skateboard, and Geoff Ho, who spent almost two weeks in hospital after being stabbed in the neck as he shielded his friends."
Those killed in the attack were Canadian Christine Archibald, 30, James McMullan, 32, from Hackney, Frenchmen Alexandre Pigeard, 26, Sebastien Belanger, 36 and Xavier Thomas, 45, Australians Kirsty Boden, 28 and Sara Zelenak 21, and Spaniard Ignacio Echeverria, 39.
Mrs May said the range of nationalities was "a reflection of our great cosmopolitan capital, whose energy and values brings together people from across the world, and a tragic reminder that the threat from terrorism transcends borders and impacts us all".
She added: "My message to those who seek to target our way of life or try to divide us is clear - our resolve to stand firm and overcome this threat together has never been stronger."
Mayor of London Sadiq Khan said the city would honour the victims of terror attacks "through our actions and standing united against terrorism and in hope for the future".
He said: "Our city faced some incredibly difficult times last year, with the terrorist attacks in Westminster, London Bridge, Finsbury Park and Parsons Green.
"The cowardly terrorists who commit these horrific acts do so to try to divide us, to fuel fear and to change how we treat one another. I'm proud of the way we have responded: standing united in defiance and staying true to our values and way of life."
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