How do I safely connect these two?

[BrendonNero]

As seen in the pictures, I need the pigtail style connected to the other style. It needs to be fully weather proofed and safe as this is wiring for a light bar on my Jeep Wrangler. So please let me know how to safely do so, rather than just shoving the two together! Thanks in advance

 

[Mike Johnson]

Insulated spade connectors crimped onto the wires and then enclosed in a waterproof junction box.

 

[telectrix]

male spades onthe bare wires then self amalgamating tape to waterproof.

 

[DPG]

Do they need to be removable? If not then I would cut the connectors off and solder the joints. And use heatshrink sleeving (ideally adhesive-lined) over each joint, and then over the lot. This will be the most reliable and weatherproof method.

 

[Zerax]

If you want it demountable... then as Tel says + some contralube inside it all before you tape it up. If it can be a permanent connection... then I'd do a proper solder joint before heat shrinking it.