The 60-year-old Thai billionaire was among five people killed when his helicopter crashed shortly after taking off from the King Power Stadium on Saturday evening.
The Foxes have postponed Tuesday's Carabao Cup game at home to Southampton, but the book will be available in a marquee outside the club shop from 8am until 10pm "for the foreseeable future".
An online book will be available via the club's website for those who cannot make it in person.
"The club would like to thank supporters for their overwhelming support and kind wishes since the tragic events of Saturday evening," a Leicester statement concluded.
On Monday, son and vice chairman Aiyawatt Srivaddhanaprabha was joined by his mother and Vichai's wife Aimon at the ground as they laid a wreath during an emotional morning.
Club officials, including director of football Jon Rudkin and chief executive Susan Whelan, also attended as they viewed the floral tributes.
The president of the Thai FA Somyot Poompanmoung and his wife, Potjaman Poompamoung, were among the group.
The first-team squad, along with manager Claude Puel, then spent 10 minutes looking at the tributes on Monday afternoon.
Goalkeeper Kasper Schmeichel, who was visibly emotional, reportedly saw the incident and raced to the scene.
Leicester's City Hall and County Hall will also light up in blue this week to honour Srivaddhanapradha, as well as Nusara Suknamai, Kaveporn Punpare, Izabela Roza Lechowicz and pilot Eric Swaffer.
Mayor, Sir Peter Soulsby said: "The outpouring of grief we are seeing at the King Power stadium demonstrates just how much the people of Leicester have taken Vichai and his family to their hearts."
Meanwhile, former Leicester and England goalkeeper Peter Shilton has described the moment he and wife Steph saw the helicopter crash.
He told the BBC: "It started to drop a little bit and then it crashed. It all seemed to happen so quickly. Then there were sparks coming out of the back, then some small flames then large flames.
"This all happened very quickly, and it all of a sudden just blew up.
"My wife became hysterical, I was in shock and think I still am, and I just grabbed hold of her.
"We were just so helpless. But at the time, thinking the chairman and his family were on there, it was just incredible.
"It is something that will live with us forever really. It is one of the most horrendous things that anyone could ever see."
Claudio Ranieri, who led the Foxes to the Premier League title in 2016, said he was "terribly shaken" by the news.
He told Sky in Italy: "He was a good man and always had a positive word for everyone. His positivity and ability to make everybody love him was clear for all to see.
"He came into the dressing room only to dispense kind words, never to reproach you.
"One time, soon after my birthday, he arrived in the dressing room with a huge cake and made everyone sing 'Happy Birthday'. He was an illuminated man and everything he touched became better.
"Now it's up to his son (Aiyawatt), who has always been in love with football, to carry on in his father's footsteps."
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