His family have described the 48-year-old as a "wonderful dad and husband, a loving son, brother and uncle", and a chapel service was held in the House of Commons.
Prime Minister Theresa May said the PC, who was married with a five-year-old daughter, "was every inch a hero".
The Metropolitan Police Force called him "a fantastic member of staff".
A minute's silence was held at 09:33 GMT in the Palace of Westminster and at New Scotland Yard.
The Rev Rose Hudson-Wilkin led the prayer and vigil service at the House of Commons Chapel of St Mary Undercroft.
Offering prayers "for Keith, our brother and all others affected", the Rev Hudson-Wilkin urged dozens of attendees "to show mercy in the face of the hatred shown in the Westminster terror attack."
A statement released by PC Palmer's family went on to say he was "a long-time supporter of Charlton Athletic. Dedicated to his job and proud to be a police officer, brave and courageous. A friend to everyone who knew him.
"He will be deeply missed. We love him so much. His friends and family are shocked and devastated by his loss."
Charlton Athletic responded to the news by putting a football scarf on PC Palmer's season ticket seat at the Valley stadium and said it would remain there until the next home game on 4 April.
There are also plans to commemorate his life at the game itself.
"Keith was a familiar face at The Valley to many supporters and sat in his same East Stand seat for many years," the club said.
"He was a true hero who will be greatly missed by all the Charlton family and everyone at the club would like to offer their sincere condolences to his family and friends at this extremely difficult time".
PC Palmer joined the Parliamentary and Diplomatic Protection Command in April last year after serving in the Territorial Support Group (TSG) based in Catford but working across London. He had previously been based in Bromley borough between 2002 and 2009.
PC James Aitkenhead, who worked alongside Keith in the TSG, said: "Keith was a genuinely nice person; nobody had a bad word to say about him. When I heard what had happened I knew it would be him because that's just the sort of guy he was, to step straight in when others might step back.
"He had a great work ethic, he worked on our warrants' car for years, getting up at 04:00 to serve warrants and arresting wanted offenders. He was always so positive, always staying late after everyone else and getting in early.
"In his personal life he was a massive Charlton Athletic fan and had a season ticket.
"We will miss him so much."
PC Palmer was nominated in 2015 for best thief taker in the Commissioner's Excellence Awards, having made more than 150 arrests in 12 months.
Insp Mark Turner said he was "a solid, reliable member of the team - he came in and just got the job done, quietly and efficiently".
"He was a fantastic member of staff and will be sorely missed."
As a mark of respect PC Palmer's shoulder number - 4157U - will be retired and not reissued to any other officer.
Tributes have been paid to Keith Palmer, the police officer killed in Wednesday's attack in Westminster.