Ray Dare died when his bike and a van were involved in a collision on the A41 Ashton Clinton bypass, near Aylesbury, Buckinghamshire, at about 14:45 BST on Wednesday.
He had belonged to the Surrey-based Kingston Phoenix Road Club for more than 60 years.
A statement on the club's website expressed "huge sadness and shock".
It said Mr Dare had been "attempting to set a new national record for a 91-year-old".
A post on the Timetrialling Forum said: "Other riders have spoken of him riding well and steadily before.
"As yet there are no further details but police, of course, are conducting a fatal accident investigation.
"I am sure all riders will be as shocked as the officials were at this news."
Circumstances surrounding the crash are being investigated and Thames Valley Police is appealing for witnesses to come forward.
The driver of the van was uninjured. No arrests have been made.

The five-storey Bursledon Windmill had its wind shaft and sails replaced following a £94,000 Heritage Lottery Fund (HLF) grant.
Built in 1814, it is believed to be the only working windmill in England that retains a wooden shaft.
Miller Jonathan Cook said it was "long-lived technology that works as well as when it was invented".
It is hoped the windmill will produce its own flour again by summer 2015.
Mr Cook said: "These are important buildings, any opportunity to see a windmill restored to a working condition is great news"
The Grade II-listed structure was rescued by Hampshire Buildings Preservation Trust in the 1970s.
Annabel Cook of Hampshire Cultural Trust, which runs the windmill, said such mills were "a revolution in the way food production was carried out".
"We're hoping to bring to life what the idea of windmilling was and its importance in people's lives," she added.
The HLF funding for the latest restoration project was secured by Hampshire county, Eastleigh borough and Bursledon parish councils, as well as Hampshire Buildings Preservation Trust.
A further £47,000 came from local councils to recruit and train more volunteers in traditional milling skills and help to run guided tours, workshops and special events.
The original timber wind shaft, which drives all the mill machinery and turns the sails, is expected to become an exhibit in an on-site museum.
The building is believed to be one of 27 such windmills regularly working in Britain.

The total number of fans attending Scottish Professional Football League games, including play-offs, was up to 4,267,467 from 3,804,342 in 2015-16.
It is the first time attendances have topped the four million mark since the 2008-09 campaign (4,252,212).
"These figures are hugely encouraging," said SPFL chief executive Neil Doncaster.
"It is testament both to the hard work of clubs in attracting people to games as well as the commitment and passion of supporters of all 42 clubs.
"There is already a great level of excitement ahead of SPFL season 2017-18 with many of our clubs executing some very creative season ticket marketing campaigns to help attract even more fans to attend matches regularly.
"All of this sends out a very positive message and provides a great platform to improve the overall profile and health of Scottish football."

The 24-year-old Belgium-born midfielder has made just 23 Premier League starts since joining from Porto on a five-and-a-half-year contract in February 2016.
"Sometimes things just don't pan out as you hope," Hughes said.
"It has been a frustration for all parties involved. It's fair to say with Giannelli that things haven't quite worked out."
Imbula became Portuguese football's record signing when he joined Porto in a £15.1m deal from Marseille in July 2015.
"He hasn't quite adjusted to the Premier League," added Hughes.
"If there is interest in him then we would consider that. We haven't had any interest, in fairness, but we would look at things if the right offer came in."
A 91-year-old cyclist killed on a dual carriageway was doing a time trial to set a new national record for his age.
[NEXT_CONCEPT]
A 200-year-old windmill in Hampshire has reopened following a two-year restoration project.
[NEXT_CONCEPT]
Scottish football enjoyed an increase in attendances at league matches of over 12% last season.
[NEXT_CONCEPT]
Stoke City's £18.3m record signing Giannelli Imbula could leave the club this summer, manager Mark Hughes says.