Addressing an audience of foreign diplomats in London, the Scottish Conservative leader will say that the country will be outward looking and “will not turn in on ourselves”.
Ms Davidson backed a Remain vote in June’s referendum along with the vast majority of colleagues in the Scottish Conservatives.
She took part in one of the final live TV Brexit debates and clashed with high profile Leave campaigner Boris Johnson, now Foreign Secretary.
In her speech at the European Council on Foreign Relations, Ms Davidson is expected to say: “I want to repeat the message that many others have given in the weeks since the referendum result - from both sides of the referendum divide.
“That, while we are leaving the European Union, we are not leaving Europe, and we will not turn in on ourselves.
“Now that we are leaving the European Union, more than ever, we must prove to you that we remain that same outward facing nation which wants to play our full part... which seeks to be a beacon for the values we share - of the rule of law, freedom and solidarity with one another.
“The structures behind our relationship will change over the coming years. I am confident that the nature of our friendship will not.”
Nicola Sturgeon has repeated her call for Ms Davidson to apologise following an “offensive” comment issued by the Scottish Conservative press office referring to a former SNP MSP.
A Tory spokeswoman suggested it was “bizarre” that Christian Allard, an EU national, had an interest in a planning dispute in Banchory and had reported a Tory MSP to the parliamentary standards watchdog.
Ms Sturgeon has written to Ms Davidson calling on her to publicly retract the remark or risk undermining efforts to combat hate crime following Brexit.