The club have cited the difficulty of hosting games against the Glasgow duo as one of the reasons for the move.
In addition, they have assessed that the "lack of enthusiasm" among the home fans as another factor in their decision.
Saints' fixture with Rangers back in September attracted a crowd of 6,251. However, there were only 1,451 home fans in attendance to witness the 4-0 defeat.
The figure is the lowest home league attendance at McDiarmid Park - when taking into account just the home fans - this season. The only time there were fewer than 2,000 Saints supporters.
The move by the club will see fans from other areas of the moved to the West Stand which holds over 3,000. Those with season tickets in the West Stand will retain their seat.
St Johnstone hope it will provide the home support with greater comfort.
The statement said: "Fans are the life blood of any Football Club. None more so than our much valued Season Ticket Holders.
"For some time now, the logistics of administering the home matches involving Celtic FC and Rangers FC has been something of a challenge for the club.
"Seat allocation, ever changing fixture dates and kick off times and a noticeable lack of enthusiasm from our supporters in the fixtures themselves, have all combined to produce a marked reduction in season ticket attendees at Celtic and Rangers fixtures over the years.
"Previous incentives such as “bring a friend for £10” was introduced, but there was very little uptake on this opportunity.
"The club makes a huge effort to ensure that visiting fans do not purchase tickets for Home areas of the ground. Increased demand from away fans and the requirements of the SPFL has meant that there has been a restricted ability to provide an “open sale” of tickets to our own fans.
Proprietorial season-ticket holders
"Various efforts have been made to address the challenges posed by these matches and this has, in the past, involved the relocation of valued season ticket holders in the East and Ormond Stands to other areas of the stadium.
"Season ticket holders can be very proprietorial over their allocated seats and understandably so. Many may have held by them for a number of years and some have been in their families since the stadium opened. This is recognised and appreciated by the board.
"However, the new road and safety requirements, which involve and affect the safety aspects of these fixtures has resulted in material changes in the way in which Celtic and Rangers fixtures will require to be administered in the future.
"With this in mind, the board has carefully considered how best to deal with these challenges, taking into account the safety, comfort and interests of our fans and the overall impact on the club both from an administrative and financial perspective.
"With the foregoing in mind, the board has decided to trial the remaining matches this season against both Celtic FC and Rangers FC, with an increased allocation to away fans and all Saints fans will be accommodated in the West Stand.
"This stand accommodates in excess of 3000 fans, which going by recent analysis will be sufficient to accommodate the projected likely number of attendees from our home support.
"Existing West Stand season ticket holders will be entitled to retain their usual allocated seat. East Stand season ticket holders will be provided with alternative unallocated seating within the West Stand.
"The remaining three stands (North, East and South) will be allocated to away fans.
"The desired result of the amended allocation would be the following:
- comfort of our fans creating a partisan atmosphere
- implementation of amended traffic management
- ease of ticket sales for home fans
- increased income for the club in order to balance the increased spend on our playing squad
- in line with similar practices adopted elsewhere
"The club hopes that our valued supporters will understand the reasoning behind the introduction of this trial and the Board welcomes all feedback on the experiences of our fans at the next few matches, prior to making a decision on any long term arrangements."