From a list to a list of rules

Another way:

Thread[var -> #] & /@ values

I propose using Inner:

Inner[Rule, var, values\[Transpose], List]

This is faster than other methods presented:

SetAttributes[timeAvg, HoldFirst]

timeAvg[func_] := 
  Do[If[# > 0.3, Return[#/5^i]] & @@ Timing @ Do[func, {5^i}], {i, 0, 15}]

var = Range@70;
values = Array[Times, {500, 70}];

Inner[Rule, var, values\[Transpose], List]; // timeAvg
Map[Rule @@@ Transpose[{var, #}] &, values]; // timeAvg
Thread[var -> #] & /@ values; // timeAvg
MapThread[Rule, {var, #}] & /@ values; // timeAvg

0.009736

0.01248

0.01372

0.01248

Just do a map on the values, like this:

var = {a, b, c}
values = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}
Map[Rule @@@ Transpose[{var, #}] &, values]

This is the output: {{a -> 1, b -> 2, c -> 3}, {a -> 4, b -> 5, c -> 6}, {a -> 7, b -> 8, c -> 9}}

(In your question you have c->5, but I'm assuming this is a mistake:)