It currently has an outstanding balance of £7.7m to pay between now and 2045 - 30 years after the first trains ran between Tweedbank and Edinburgh.
However, it has now agreed to borrow money to pay off the balance in a move estimated to save about £4.3m.
Council leader David Parker said it would reduce the burden on local tax payers.
He said the local authority had access to very low rates on its borrowing.
"When officers have looked very carefully at the financial issues around it, it makes sense to make that saving," he said.
"That is exactly what we will be doing now.
"For future councils we are reducing the revenue burden on them and making sure that the railway contribution is paid."

Winger Ashley Young and debutant defender Reece James, 20, also scored two goals each after striker Danny Welbeck had opened the scoring.
Van Gaal,  made United's longest-serving player, midfielder Darren Fletcher, captain for the pre-season friendly, the first of four games on the club's US tour.
The Dutchman, who led the Netherlands to the semi-finals of the 2014 Fifa World Cup, saw another debutant, Ander Herrera, dictate proceedings in midfield with a good range of short and long passes delivered crisply and accurately.
Van Gaal marked his arrival at the Pasadena Rose Bowl with some almost magisterial waving to United supporters as the team coach approached the stadium which hosted the 1994 World Cup final.
It was nothing like the tentative manner with which Moyes had approached the same task 12 months earlier.
The change could be seen in Van Gaal's first starting line-up. Only two players survived from the team Moyes saw beaten 1-0 by Singha All Stars in Thailand a year ago - defender Jonny Evans and Welbeck.
There was also a new 3-4-1-2 formation, with debutant Luke Shaw - a £27m buy from Southampton this summer - and Antonio Valencia operating as wing-backs either side of a three-man central defence and Juan Mata in an advanced midfield role.
Van Gaal used the same tactic to steer Netherlands to third place in Brazil.
There were few signs of emotion from the 62-year-old when striker Welbeck put his side in front with a first-time finish from 20 yards.
Welbeck had been one of the players he had been urging to "look at the ball" during shooting practice in Tuesday's training session.
But even after the England man had drilled home the loose ball once Mata had been fouled, Van Gaal restricted himself to a raised right fist as he rose to acknowledge the first goal of his reign.
Overlooked for the captaincy after Fletcher was handed the armband, Rooney doubled the visitors' lead from the penalty spot three minutes before the break.
By the time he strode purposefully down the tunnel at half-time, Van Gaal had seen his team score again, Rooney profiting from Tommy Meyer's abysmal defending, and he had also been in animated discussion with the fourth official over an incident that had evidently angered him.
Bacup-born left-back James, who was on loan at Carlisle last season, reacted joyously to both his goals and, as Galaxy's defence fell apart, Young scored twice in as many minutes at the end.
In changing his entire team during the interval, apart from midfielders Fletcher and Herrera, Van Gaal made good his promise to look at everyone before deciding who needs to be kept and who will be released.
United's next friendly will be against Roma in Denver on Saturday.
LA Galaxy (4-1-3-2) Penedo; Gargan, Meyer, Leonardo, DLG; Ishizaki, Sarvas, Juninho, Husidic; R Keane, Zardes
Manchester United (3-4-1-2) De Gea; Smalling, Jones, Evans; Valencia, Fletcher, Herrera, Shaw; Mata; Rooney, Welbeck.
Second-half - (5-3-2) Lindegaard; Rafael, M Keane, Fletcher, Blackett, James; Herrera, Cleverley, Kagawa; Young, Nani.
Scottish Borders Council has agreed a move to cut the overall cost of its contribution to the Borders Railway.
[NEXT_CONCEPT]
Manchester United's new manager Louis van Gaal made a winning start as Wayne Rooney scored twice in a 7-0 defeat of LA Galaxy in front of a crowd of 86,432 at the Rose Bowl in California.