Single Board Computer (SBC) suggestion for interfacing with DMA
Your numbers suggest a bandwidth of roughly 53.4 MB/s (MegaBytes!). This makes me wonder about the requirements for the rest of the system given that you want to add the overhead of a heavy Linux OS like Ubuntu on top.  For what it's worth, there are some SBC Linux boards that offer DMA to a memory card reader to achieve somewhere in the neighborhood of 6 MB/s - this figure probably does not take protocol overhead in to account so the actual data throughput is probably less.  Your calculation however, is all raw data, which adds even more to the challenge.

I'm curious to know what kind of application requires that high of a sampling rate - I can imagine something like high frequency radio transceivers need something this fast (or faster) but I won't speculate as to what you're using this for - high speed data acquisition (if this is even really considered high-speed) is not within my knowledge.

Given the bandwidth requirement, what I would do is start with a computer peripheral bus that is capable of moving that kind of data.  


PCI: 133 MB/s 
PCIe (1-lane, gen1): 250 MB/s 
If you're willing to decrease your sampling rate, USB 2.0: 480 Mbit/s
(effective throughput up to 35 MB/s)


These figures may or may not include protocol overhead, so keep in mind that your calculated required bandwidth is already pure data and may require much more than 53.4 MB/s considering protocol overhead.

For now I'm going to forget the requirement of an SBC and suggest a full blown PC. After choosing the right bus, now you have the pleasure of implementing your own peripheral card to plug in to a typical PC capable of running Ubuntu. You'll have to write a linux driver for your custom PCI/PCIe/USB device too. I'm hoping someone replies with a nice SBC that exposes a memory bus with DMA instead... the above solutions will surely be a challenge.

By the way, what was already processing the data after the FPGA in the first place? Was it not good/flexible enough?