The "Gravity Radar" Each object forms a gravity well in space-time. Okay, two objects are approaching each other at nearly the speed of light. How do they pick up each other's "gravity radar" signals in order to form a common unified gravity well and be attracted to each other?
 A: It works in the same way that light travels. If you're familiar with special relativity, then you'll know that when two observers are moving towards each other at close to the speed of light it will still be 'c' in their reference frame. 
The same is true for gravitational waves. From each persons perspective, the gravitational waves will propagate at the speed of light. 
If you're interested in the mechanism on how that works, read up on special relativity.
A: They don't need to sense each other by radar like methods. They don't need to send out signals, it's a one way system, they get pulled together when gravity is strong enough to overcome any other velocity they might have.
They  meet up in somewhat  the same way as the Earth goes around the sun. Spacetime is curved (in a way that every picture you have seen does not represent accurately, because we cannot visualise four dimensions, so "gravity well" might give you a wrong idea, only math can really describe it) .
They follow geodesics, which are the paths of shortest distance in spacetime, but because spacetime is curved, they are not always straight lines.
For the situation you describe, they will be pulled together in a way that makes the distance of travel in the  4D spacetime between them as short as possible.
Luckily in the case of the Earth, our path is curved around the sun, rather than straight at it, because of the way our velocity vector is pointed.
