Estonia is the second of the three Baltic States, after Lithuania, to ink a border pact with Russia. Difficult negotiations are under way with Latvia.
Speaking after the signing of the two agreements demarcating both land and sea borders, Lavrov said Estonia had pledged not to question the terms of the treaty.
"Before signing the treaty, our Estonian colleagues assured us that they would not make any unilateral interpretations of this treaty as to where the border lies," Lavrov said.
Estonia had previously demanded that the border with Russia be determined according to a 1920 treaty that attributed to Estonia some territories that were subsequently handed over to the Soviet Union after World War II.
Ehtel Halliste is the spokeswoman for Estonia's Foreign Ministry. She told RFE/RL by telephone that Estonia hopes the treaty will boost ties with its Russian neighbor:
"Of course we are satisfied that finally these agreements have signatures. We also hope that the signing of these two treaties will create a good basis for the further development of Estonian-Russian relations," Halliste said.
The draft border treaty between Russia and Estonia had been ready since 1996, but Russia long refused to sign it.
Russia's foot-dragging on the border settlement was widely seen as an attempt to sway Estonia into granting more rights to the large community of Russian speakers still living in the former Soviet republic.
Dmitry Trenin is an expert at the Carnegie Center in Moscow. He says that by refusing to sign the treaty, Russia also sought to impede the entry of the Baltic States into the European Union.
"Russian once hoped that stalling the border question with Russia would slow the entry of the Baltic States into NATO and the European Union. This did not happen. The lever that Russia thought it had in hand did not prove efficient," Trenin said.
The Baltic states' entry into the European Union last year may explain why the Kremlin invited Paet to sign the border agreement earlier this month.
Trenin says Russia now has an interest in officially fixing its border with the Baltic states, which now constitute the European Union's most eastern countries.
"Now that the Baltic States have joined the NATO and the European Union, there is both a possibility and a need to finally, officially, solve the border issue and thereby fix not only the Russian border with Estonia and Latvia, but also with the European Union, Russia's most important partner in the West," Trenin said.
The absence of border treaties with the Baltic countries hampered the easing of EU visa rules for Russian citizens, which Russia has been eager to obtain.
It also hurt trade between Russia and Estonia, as both stalled some 20 bilateral trade accords until the signature of the border treaty.
The Baltic states are not the only countries working to sign border treaties with their Russian neighbor -- such agreements have been signed with China and are under discussion with Kazakhstan and Ukraine.
Trenin says that Russia's efforts to officially demarcate borders with all its neighbors is part of a Kremlin campaign to consolidate Russia's territorial integrity.
"Russia's territorial integrity and its sovereignty on all its territory are President Vladimir Putin's most important values. To obtain such sovereignty and territorial integrity, Russia needs fixed agreements with its neighbors. This is part of Putin's policy to build the state," Trenin said.
The new treaty introduces only minor changes to the current border that was established when the Soviet Union occupied the Baltic states after World War II.
The treaty must be ratified by the parliaments of both countries to come into force.