How to make a worldborder that expands every in-game day at dawn?

First place a daylight sensor with a comparator infront of it, with the comparator facing out of the daylight sensor. Then put a command block as the output of the comparator. The redstone should look like following:

Then, inside the command block, type:

/worldborder add 2

How this works is that the daylight sensor will activate each day and when it activates, it will give an input to the comparator which will then execute the command inside the command block and add a distance of 2 to the world border.

Plan 1: (hard&redstone way, no big differences with Plan 2) (not tested)
First of all, you must do a 1 day loop with redstones. And next off, when you connect them to the command block, you must add /worldborder add 2 1 (2 = 2 blocks, 1 = 1 seconds to open) to it.

Plan 2: (easy way) (tested and works)
Put a Daylight Sensor, connect it to a command block, add /worldborder add 2 1 (2 = 2 blocks, 1 = 1 seconds to open) in command block.

Note: Plan 2 might not work, see CommandFox' answer for a better take of this plan.

Plan 3: (tested and works) (world will grow slowly, a new block everymidday)
A minecraft day is 20 minutes. 1200 seconds. So just use this code in console: /worldborder add 2xdays-you-want 1200xdays-you-want. So making this work for 1000 days would be /worldborder add 2000 1200000.

Also if you are mapping, I recommend adding another command block to let the player know that world grew.