Let's say I take a software (Work) distributed under GPLv3 compatible license, and create a Derivative Work. Can I distribute it (the Derivative Work) under GPLv3 license? If not, how can I make a Derivative Work part of a project distributed under GPLv3?
In brief, yes.
The very definition of a GPLv3-compatible licence is that "you can combine code released under the other license with code released under the GNU GPL in one larger program". If you are not the rightsholder in the GPLv3 code, then (by GPLv3 s5c) you must release the entire derivative work under GPLv3. Since in this case you are the rightsholder, you do not have to do that, but you very clearly may.
Unless the original license explicitly allows it, you can not drop the license of the original Work and replace it with the GPLv3. What you can do is that you license your modifications under the GPLv3 license.
Although the GPLv3 requires that you distribute the entire Derived Work under the GPLv3 license, it does not give you permission to go against the requirements of the original license. For a GPL-compatible original license, this means in effect only that you can't just throw away the original license text. (Although, officially it means you need to comply with the requirements of both licenses where it comes to code that was part of the original Work.)