The club has also confirmed it’s first three pre-season friendlies.
Walker, who is 24, joins the club after a two-year spell with Livingston, where he spent most of his time on the bench, although he did make seven senior appearances for the West Lothian side.
He was ruled out of the majority of the first half of Livingston’s 2014-2015 campaign, with former Berwick stopper Paul Grant brought in on a short-term deal to cover for his injury during his time out.
However, upon returning, Walker reclaimed his place in the squad and found himself a part of the side which went on to avoid relegation and win the Petrofac Training Cup in April.
McKenna also joins Rangers from Livingston, where he was a much more regular part of the Lions’ squad.
Last season he played 33 times, mainly filling a position on the left side of midfield.
He was previously involved in the youth set-up at Celtic, Hearts and Hibernian and spent some time with Musselburgh Athletic in 2014 before joining Livi.
He is also an ex-Scotland Junior international.
Both players will now be looking to earn a regular place in Colin Cameron’s starting line-up at Shielfield.
Meanwhile, Berwick have confirmed another three pre-season friendlies, two of which will be played at home.
Rangers, who have already announced a clash with FA Vase holders North Shields at Shielfield on Saturday, July 4, will take on Scottish Premier League opposition in the shape of Kilmarnock, who will visit Shielfield on Saturdsay, July 11, with a 3pm kick-off.
Three days later, on Tuesday, July 14, Cameron’s men will host Championship opposition, going up against Hibernian’s first team. This game is scheduled to kick off at 7.45pm.
Berwick will then hit the road as they travel to Station Park on Saturday, Jul6y 18, taking on Forfar Athletic in a 3pm kick off.
Admission prices will be confirmed closer to the time of the fixtures.