Using jQuery:

var str = '{"id":1,"name":"Test1"},{"id":2,"name":"Test2"}';
var jsonObj = $.parseJSON('[' + str + ']');

jsonObj is your JSON object.

Script for backward-compatibility: https://github.com/douglascrockford/JSON-js/blob/master/json2.js

And call:

var myJsonString = JSON.stringify(yourArray);

Note: The JSON object is now part of most modern web browsers (IE 8 & above). See caniuse for full listing. Credit goes to: @Spudley for his comment below

You just need to run this through JSON.parse(), which is supported by almost all the JavaScript parsers:

console.log(JSON.parse(`[  
    [32.361346650846805,50.90932315437885],
    [32.36743646734031,50.95189517586323],
    [32.35467638118774,50.95876163094135],
    [32.342494619322636,50.904516635824166],
    [32.36279664436138,50.90039676277729],
    [32.380194752587755,50.899023471761666],
    [32.3648265962154,50.91481631844135],
    [32.361346650846805,50.90932315437885]
]`));

Just beware that the JavaScript might not like having line-breaks in strings if you give them in source code. If the original string does have line-breaks, that's totally fine. That's why I have used a template literal here.

// Say you have your string here.
var str = `[  
    [32.361346650846805,50.90932315437885],
    [32.36743646734031,50.95189517586323],
    [32.35467638118774,50.95876163094135],
    [32.342494619322636,50.904516635824166],
    [32.36279664436138,50.90039676277729],
    [32.380194752587755,50.899023471761666],
    [32.3648265962154,50.91481631844135],
    [32.361346650846805,50.90932315437885]
]`;
// Convert to array.
var arr = JSON.parse(str);
// Loop throught the array.
for (var i = 0; i < arr.length; i++)
  console.log(arr[i]);